https://github.com/floatingpragma/observer-patch-holography
Observer Patch Holography is the observer-consistency theory of everything. No observer sees the whole world at once; each observer gets a local patch; physics is the public fixed point that survives agreement across overlaps.
https://github.com/floatingpragma/observer-patch-holography
general-relativity holographic-principle physics quantum-computing quantum-gravity-foundations standard-model
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Observer Patch Holography is the observer-consistency theory of everything. No observer sees the whole world at once; each observer gets a local patch; physics is the public fixed point that survives agreement across overlaps.
- Host: GitHub
- URL: https://github.com/floatingpragma/observer-patch-holography
- Owner: FloatingPragma
- License: other
- Created: 2026-01-18T05:41:45.000Z (5 months ago)
- Default Branch: main
- Last Pushed: 2026-06-08T10:12:44.000Z (5 days ago)
- Last Synced: 2026-06-08T10:19:40.055Z (5 days ago)
- Topics: general-relativity, holographic-principle, physics, quantum-computing, quantum-gravity-foundations, standard-model
- Language: Python
- Homepage: https://floatingpragma.io/oph
- Size: 221 MB
- Stars: 530
- Watchers: 7
- Forks: 65
- Open Issues: 34
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Observer Patch Holography (OPH)
> Observer Patch Holography is the observer-consistency theory of everything. No observer sees the whole world at once; each observer gets a local patch; physics is the public fixed point that survives agreement across overlaps.
**French version:** [README_FR.md](README_FR.md)
**Quick links:** [OPH website](https://floatingpragma.io/oph/) | [OPH Textbooks](https://learn.floatingpragma.io/) | [Reverse Engineering Reality](https://oph-book.floatingpragma.io/) | [OPH Lab](https://oph-lab.floatingpragma.io) | [Applications](https://omega.floatingpragma.io/) | [OPH Blog](https://blog.floatingpragma.io/) | [Coherence map](https://coherence.floatingpragma.io/) | [Three-body demo](https://3body.floatingpragma.io/)
**Falsifiability:** [OPH falsifiability map](extra/OPH_falsifiability.md)
lists 40 hard OPH-killing outcomes and concrete IBM Quantum Cloud tests for
the reduced-sector hardware signature. Falsifiability is how a physics theory
pays rent. OPH is highly falsifiable: a massive graviton, a gauge-mediated
proton decay event, a fourth light matter generation, a charge-lattice outlier,
or neutrino data excluding the OPH branch would destroy OPH as stated.
If you want the existential answer first, jump straight to **Paper 6.
[Paradise as Fixed-Point Consensus](paper/paradise_as_fixed_point_consensus.pdf)**.
The short version is direct: yes, this universe is a simulation in the OPH
sense, an observer-based fixed-point consensus process. Yes, subjective
experience and minds are primary. Yes, space, time, and matter are
observer-facing appearances: stable effective structures generated by deeper
patch consistency. The illusion metaphor is handled below. The rest of this
README gives the mathematical proof stack and empirical verification surface.
OPH is the observer-first reconstruction of fundamental physics. It starts from
finite observers on finite holographic screen geometry. Its working basis is
quantum-algebraic: patch algebras, states, trace/Born event probabilities on
declared record surfaces, and generalized entropy are part of the formal
starting point. From that basis, OPH recovers the observed effective universe:
spacetime, gauge structure, particles, records, and observer synchronization all
follow from overlap consistency. At the operating level, finite observer
patches carry local records, compare only what their overlaps expose, repair
mismatches through declared recovery moves, and settle into stable fixed points
that survive refinement. The public world is the overlap-stable output of that
process. This is the mathematical and empirical proof surface for OPH as the
correct theory of everything: the same observer-consistency architecture
recovers the established physics and explains why a world exists that can
produce observers capable of reconstructing it.
OPH is formulated as a zero-input theory. Its quantitative surface uses two
dimensionless closure coordinates and one selected no-G scale certificate, all
fixed by closure:
$$
P_\star=\varphi+\frac{\sqrt{\pi}}{A_T(P_\star)}
$$
for the local pixel ratio, and
$$
N_{\mathrm{CRC}}=F(N_{\mathrm{CRC}})
$$
for the global screen capacity, where $F(N)$ is the active horizon capacity read
back by observers inside the universe supplied with capacity $N$. The selected
scale certificate is most cleanly written as a dimensionless clock ratio,
$$
\gamma_\star=\frac{\ell_\star\nu_{\mathrm{Cs}}}{c},
\qquad
B_\star=\frac{3\pi}{\ell_\star^2},
\qquad
G_{\mathrm{SI}}=\frac{c^3\ell_\star^2}{\hbar}.
$$
The finite count representation of the global capacity closure is
$$
N_\star=\mathrm{MAR}\,\mathrm{argmax}_{N}
\bigl(\log|\Omega^{\mathrm{sc}}_N|-N\bigr)
$$
Informally, $N_{\mathrm{CRC}}$ is the unique capacity where the universe reads
back its own boundary without deficit or slack. In geometric units the
cosmological readout is
$$
\Lambda_{\mathrm{CRC}}=\frac{3\pi}{G_{\mathrm{geom}} N_{\mathrm{CRC}}},
\qquad
G_{\mathrm{geom}}=\ell_\star^2.
$$
The recovered electromagnetic branch gives Maxwell's equations on the ordinary
photon lane. The fine-structure and particle rows sit downstream of $P_\star$ and the
recovered structural branch. The cosmological row sits downstream of
$N_{\mathrm{CRC}}$. The Newton normalization sits downstream of
$\ell_\star^2=3\pi/B_\star$.
Observation is used for reverse engineering. Because OPH treats the universe as
a closed mathematical fixed structure, approximate measured values can locate
the basin or observed branch. The precise OPH value must come from the declared
fixed-point map and its Banach contraction, derivative-sign, strict-concavity,
or equivalent uniqueness certificate.
The two dimensionless closures fix dimensionless geometry. In particular,
$\Lambda_\star\ell_\star^2=3\pi/N_{\mathrm{CRC}}$ and
$\Lambda_\star a_{\mathrm{cell}}=3\pi P_\star/N_{\mathrm{CRC}}$. A selected
scale certificate supplies the SI scale product
$B_\star=\Lambda_\star N_{\mathrm{CRC}}=3\pi/\ell_\star^2$.
In the informal simulation-language reading, $P$ links the pixel area of the
simulating-side screen to the electromagnetic interaction, i.e. observation, in
the simulated-side universe. It gives $P\simeq1.630968$ and the low-energy
fine-structure value near $1/137$. $N_{\mathrm{CRC}}$ links the outside total
horizon capacity to the inside observer-accessible public record: the universe
must be able to reconstruct its own boundary. The gravity scale is read on its
own observed branch through the no-G scale certificate $\gamma_\star$, or
equivalently $B_\star$, after which $\ell_\star$ is displayed as the Planck
length. Observers inside infer
geometry, horizons, entropy, $\Lambda$, history, and records from information
available inside the universe.
## Applications And OMEGA Hardware
OPH is also a hardware program. As the screen microphysics becomes explicit,
the same patch-consensus loop becomes an engineering handle on reality. A
bounded device exposes boundary data, compares records, repairs mismatch, and
locks onto stable states. OMEGA is the public hardware route into that loop:
physical chambers, labeled ports, control software, verifier receipts, and
repeatable records.
In plain language, OPH turns screen microphysics into a way to hack reality.
The goal is not metaphorical control of an abstract simulation. The goal is
physical control of small patches that can be driven, measured, repaired, and
verified.
The application thesis is simple. If reality is built from observer-patch
consistency, then useful machines can be built by driving small physical
patches into the right fixed points. That gives low-cost implementation tracks
for desktop fusion energy, room-temperature OMEGA supercomputing, OMEGA-based
AGI, and local gravity or inertia control for hoverbikes and hoverboards. These
are application tracks behind evidence gates, not theorem outputs. The current
compute claim is the narrower exact-verifier claim: a chamber-conditioned
candidate distribution may reduce verifier work by a measured lift
`B = p_Q/p_U`; it is not a complexity-class theorem.
Read the public applications page at
[omega.floatingpragma.io](https://omega.floatingpragma.io/). Source notes for
the application tracks live in [`APPLICATIONS.md`](APPLICATIONS.md). The local
gravity and inertia track also has a standalone engineering note:
[Hacking the Simulation: Anti-Gravity Exploit](https://github.com/FloatingPragma/oph-meta/blob/main/docs/oph-gravity-hack/hacking-the-simulation-anti-gravity-exploit.pdf).
## The Spacetime Trap
The first conceptual hurdle is that OPH does not treat spacetime as the
container in which reality happens. Space and time are not things in themselves.
They are stable observer-facing descriptions that appear when many finite
perspectives can be made mutually consistent.
Some would call this an illusion. As a metaphor, that is fair: the container we
seem to inhabit is an appearance produced by deeper consistency. As physics,
the sharper phrase is emergent public description.
From inside one perspective, the world feels obvious. There is a roughly
spherical field of experience stretching outward, three directions to move in,
and time passing forward. Other observers report compatible contents from
different angles, so the natural guess is that everyone lives inside one
pre-existing spacetime filled with objects. OPH reverses that guess. Each
observer has a local spacetime description generated by its own accessible
records, clocks, horizons, and correlations. The public spacetime is the
compatibility layer that lets those descriptions agree.
This does not make ordinary spacetime arbitrary or useless. It explains why it
works so well. Einstein's equations describe the smooth large-scale grammar of
the shared appearance. The deeper claim is that the shared appearance is
emergent from observer overlap consistency, not part of the world's starting
inventory.
## What OPH Delivers
Most theories begin by assuming spacetime, quantum fields, and a list of
constants. OPH starts one step earlier than spacetime and quantum field theory,
with finite observers on finite quantum-algebraic holographic screen geometry
whose descriptions have to agree where their patches overlap. Push that
requirement through the support-visible BW/geometric scaling branch and a
3+1-dimensional Lorentzian spacetime emerges, together with a Jacobson-style
Einstein equation. Finite cells serve as the regulator. The Lorentz branch is
the extracted prime geometric cap-pair limit with fixed-collar Markov/recovery
remainders carried through regularized
modular transport, support-readable modular covariance, and KMS/BW
normalization. In the gauge lane,
zero-obstruction is a transportability condition: it reconstructs a compact
gauge group from the persistent sector category, but does not by itself select
the Standard Model. MAR plus the explicit one-Higgs matter package selects the
realized Standard Model quotient $SU(3)\times SU(2)\times U(1)/\mathbb Z_6$,
including the exact hypercharge lattice, the realized color triplet $N_c=3$,
and the generation count $N_g=3$. Quantum mechanics is the algebraic
information language carried by the OPH architecture.
On the declared support-visible compact-gauge branch, with four-dimensional
scaling, reflection positivity, repair completeness, and support-visible
continuum extraction in force, the same stack gives the Euclidean Yang-Mills
form and identifies the Yang-Mills mass gap with the repair gap. This is OPH's
four-dimensional axiomatic Yang-Mills construction on the declared branch.
Clay-facing admissibility is branch-dependent and turns on taking that
support-visible continuum extraction as the required four-dimensional
construction.
The mechanism is the fixed-point consensus loop. Local observers do not access
a global state from outside. They carry finite patch states, exchange
overlap-visible data, reject inconsistent continuations, and keep the stable
patterns that can be synchronized. Geometry, particles, laws, and records are
the large-scale fixed points of that observer-network computation.
## Geometry, Symmetry, and Simulators
Sphere language in OPH is geometry language. In symmetric regulator charts, an
observer-accessible cut can be represented by the two-sphere $S^2$. Those
charts describe angular support geometry. The finite simulator implements the
patch-and-overlap algebraic constraints exposed by that geometry.
OPH therefore uses one shared screen net idealization and many finite observer
patches. An observer screen is a local access cut on that net, not a separate
private sphere. The $S^2$ chart is not a literal ball with data painted on it.
That spherical chart carries several concrete jobs. Caps and collars give the
local cut data used by modular flow and entropy variation. The conformal group
of the sphere is the celestial-sphere form of the connected Lorentz group,
$\mathrm{SO}^+(3,1)$, so the same chart supplies the kinematic bridge to the
emergent $(3+1)$-dimensional spacetime branch once the support-visible cap
modular theorem is satisfied. Spherical harmonics organize angular modes.
Finite cellulations of the same chart give the regulator surface on which patch
ports, edge data, and overlap checks can be made explicit; they are not by
themselves a Lorentz-invariant continuum.
The finite symmetry anchor is $A_5$, the rotational symmetry group of the
icosahedron. It supplies the icosahedral skeleton behind the echosahedral patch
carrier language: a finite, highly symmetric way to organize ports, overlaps,
and local comparison data without treating the carrier as a smooth ball.
The exceptional symmetry anchor is the $E_8$ Lie group and its root-lattice
structure. $E_8$ matters because it gives the exceptional closure language
used in the higher symmetry and representation side of the OPH stack. The
binary icosahedral group and affine $E_8$ meet through the McKay
correspondence. This is why $A_5$-icosahedral and $E_8$-type language can
belong to one symmetry story. These names mark symmetry constraints and
regulator structure.
The scale story has three roles: a global capacity closure, a local pixel
closure, and a no-G scale readout. The global coordinate is the unique cosmic
record-closure capacity,
$$
N_{\mathrm{CRC}}=F(N_{\mathrm{CRC}}),
$$
where the supplied horizon capacity and the observer-readback capacity agree.
The finite-count target is the density
$$
\log|\Omega^{\mathrm{sc}}_N|-N.
$$
On the observed branch this fixed point is the de Sitter entropy capacity. For
the observed cosmological constant, the bare horizon area ratio is about
$1.05\times10^{122}$, while the OPH entropy capacity is about
$3.31\times10^{122}$. That displayed capacity belongs to the cosmological
branch. The local/global hierarchy-resonance bridge uses a stricter exact
condition: the electroweak projection target corresponds to
$N_{\mathrm{EW}}(P_\star)=3.5323546226929906511187512962330547600462\times10^{122}$
on the public endpoint branch, and the rounded capacity display is not an exact
bridge certificate. The Newton row uses the same fixed-point capacity together
with the selected no-G scale certificate.
The local coordinate is the pixel ratio
$$
P=\frac{a_{\mathrm{cell}}}{\ell_\star^2},
\qquad
\ell_\star^2=\frac{3\pi}{B_\star}.
$$
The scale certificate supplies $\ell_\star^2$; only after that readout is the
area displayed as the Planck area. From the outside, $P$ is a geometric
cell-size ratio slightly above the golden-ratio self-similar balance. From the
inside, the same cell is the smallest electromagnetic observation scale
available to observers in the encoded universe.
The applications sit downstream of those roles. The fine-structure lane asks
for the nonzero detuning of a holographic screen cell such that the cell's
outer geometric displacement equals the electromagnetic observation scale
emitted by the universe living on that screen. The public solution is
$P\simeq1.6309682094$, with
$\alpha^{-1}(0)=137.035999177(21)$ and
$\alpha(0)\simeq0.00729735256433$. The same local pixel scale feeds the gauge
structure, scoped particle-mass rows, records, and observer synchronization. On
the gravity row it supplies
$$
a_{\mathrm{cell}}=P\ell_\star^2,
\qquad
\bar{\ell}_{\mathrm{shared}}=\frac{P}{4}.
$$
The factor $P$ cancels in the Newton area-law readout, leaving
$G_{\mathrm{geom}}=\ell_\star^2$. The particle pipeline carries the local
scale into the weak sector, the Higgs lane, selected-class quark rows, and the
weighted-cycle neutrino branch. Hadrons require either the OPH strong-binding
backend or an explicitly marked empirical hadron closure. The operating policy
for those rows is in [`HADRON.md`](HADRON.md). Hardware-facing checks of the
same fixed-point geometry are treated only as public evidence-bundle claims
when the raw artifacts and verifier receipts are available.
### Selected Quantitative Rows
This table keeps the rows that are easiest to compare directly with PDG and
NIST values. Structural results such as the 3+1-dimensional Lorentzian spacetime, the
MAR-selected Standard Model quotient $SU(3)\times SU(2)\times U(1)/\mathbb Z_6$, the exact hypercharge
lattice, the realized color triplet $N_c=3$, and the generation count
$N_g=3$ live in the papers. The
quick view here sticks to direct numeric rows and exact zeros.
| Quantity | Symbol | OPH | PDG/NIST | Δ |
| --- | --- | --- | --- | --- |
| Gravitational constant | G | 6.6742999959e-11 | 6.67430(15)e-11 | 0.00003σ |
| Speed of light | c | 299792458 | 299792458 (exact) | match |
| Fine-structure (inv) | α⁻¹(0) | 137.035999177 | 137.035999177(21) | match |
| Photon mass | m_γ | 0 eV | <1e-18 eV | below bound |
| Gluon mass | m_g | 0 GeV | 0 GeV | match |
| Graviton mass | m_grav | 0 eV | <1.76e-23 eV | below bound |
**Quark sector**
| Quark | Symbol | OPH | PDG | Δ |
| --- | --- | --- | --- | --- |
| Bottom | m_b(m_b) | 4.183 GeV | 4.183 ± 0.007 | match |
| Charm | m_c(m_c) | 1.273 GeV | 1.2730 ± 0.0046 | match |
| Strange | m_s(2 GeV) | 93.5 MeV | 93.5 ± 0.8 | match |
| Down | m_d(2 GeV) | 4.70 MeV | 4.70 ± 0.07 | match |
| Up | m_u(2 GeV) | 2.16 MeV | 2.16 ± 0.07 | match |
| Top | m_t cross-section row | 172.35235532883115 GeV | 172.3523553288312 | selected-class match |
$\Delta$ reports the sigma distance where PDG or NIST quotes a one-standard-deviation
uncertainty. Otherwise it records "match" or "below bound".
For quarks, PDG uses its standard mass conventions: `u`, `d`, and `s` at
`2 GeV`, with `c` and `b` in the `MS` scheme at their own mass scale. The
papers also carry the structural Standard Model derivations listed above and a
neutrino family, but those do not collapse to one simple PDG or NIST row and
are left out of this table.
The particle surface also reports $W/Z$ values $80.377\,\mathrm{GeV}$ and
$91.18797809193725\,\mathrm{GeV}$, a Higgs value $m_H=125.1995304097179\,\mathrm{GeV}$, and a
selected-class top value $m_t=172.35235532883115\,\mathrm{GeV}$ using the PDG
cross-section top-mass convention. The weighted-cycle neutrino branch emits
$(0.017454720257976796, 0.019481987935919015, 0.05307522145074924)\,\mathrm{eV}$ on its
declared branch.
## Quantitative Unification Surface
The quantitative surface is organized around distinct fixed-readback roles: the
pixel fixed point $P\simeq1.6309682094$, the global record-capacity fixed point
$N_{\mathrm{CRC}}\simeq3.31\times10^{122}$, and the selected no-G scale
certificate $\gamma_\star$, equivalently $B_\star=3\pi/\ell_\star^2$. The
displayed capacity is approximate; precision rows use the fixed-point value and
the scale certificate. The $P$ branch feeds the Ward-projected electromagnetic channel
and the scoped particle-mass rows, while also fixing the cell/edge identity that
cancels out of the Newton area-law readout. The $N_{\mathrm{CRC}}$ branch feeds
the cosmological-constant readout. The scale certificate supplies the area
quantum that becomes the Newton normalization. The hierarchy-resonance bridge is
recorded as a selected-branch theorem: the finite readback-resolution
certificate, the representation-to-spectrum count $2(8+3+1)=24$, and the exact
global-capacity bridge certificate close the local/global hierarchy package.
On that selected exact branch, OPH solves the electroweak hierarchy/naturality
problem with $\epsilon_H=0$ and no measured weak-scale input.
The detailed formulas and claim tiers live in the papers.
**OPH Stack**
The main OPH line from axioms to relativity, gauge structure, particles, and observers. Click to open the full SVG.
**Particle derivation stack**
A compact view of the particle lane. Click to open the full SVG.
## Papers
- **Paper 1. [Observers Are All You Need](paper/observers_are_all_you_need.pdf)**: broad synthesis of the OPH reconstruction program, from finite observers to the recovered effective universe.
- **Paper 2. [Recovering Relativity and the Standard Model from Observer Overlap Consistency](paper/recovering_relativity_and_standard_model_structure_from_observer_overlap_consistency_compact.pdf)**: compact technical core for relativity, gravity, zero-obstruction compact-gauge reconstruction, MAR-selected realized Standard Model structure, Maxwell equations on the ordinary photon branch, and the support-visible compact-gauge Yang-Mills form/gap theorem under its declared branch assumptions.
- **Paper 3. [Deriving the Particle Zoo from Observer Consistency](paper/deriving_the_particle_zoo_from_observer_consistency.pdf)**: particle derivations, mass rows, coupling structure, and the quantitative comparison surface.
- **Paper 4. [Reality as a Consensus Protocol](paper/reality_as_consensus_protocol.pdf)**: fixed-point repair dynamics, record stability, and the consensus picture of public reality.
- **Paper 5. [Federated Echosahedral Screen Microphysics](paper/screen_microphysics_and_observer_synchronization.pdf)**: federated patch-carrier architecture, $A_5$-icosahedral and $E_8$-type symmetry framing, public hardware-evidence rules, records, recovery moves, and observer synchronization.
- **Paper 6. [Paradise as Fixed-Point Consensus](paper/paradise_as_fixed_point_consensus.pdf)**: final manifest paper for OPH's meaning layer: why anything exists, why this world is observer-compatible, the strange loop in which observers reverse engineer and build the continuation machinery, paradise on Earth or in engineered continuation environments, hell as enforced isolation or deprivation, resurrection as observer continuation, justice as continuation according to harm and repair records, and memetic evolution.
## Supplemental Papers
- **[Photonic Fixed-Point Consensus for SHA-256d Proof of Work](extra/Photonic_fixed-point_consensus_for_SHA-256d_proof_of_work.pdf)**: photonic candidate enrichment for SHA-256d proof of work.
- **[The Fine-Structure Constant as an OPH Pixel Fixed Point](extra/fine_structure_constant_derivation.pdf)**: fixed-point derivation of the fine-structure row.
- **[Observer-Patch Holography as a String-Vacuum Selector](extra/observer_patch_holography_as_string_vacuum_selector.pdf)**: OPH edge-string emergence, the Bouchard-Donagi one-Higgs heterotic witness, the `Z4R` safety layer, and moduli-locking gates.
- **[Explaining the Yang-Mills Mass Gap with Observer-Patch Repair Dynamics](extra/yang_mills_gap_clay_problem.pdf)**: support-visible OPH route to the Clay Yang-Mills problem, branch-scoped to the compact-gauge extraction, with Clay-facing status tied to that axiomatic-construction claim, and identifying the gap with the repair gap.
- **[Observer-Patch Holography and the Dark Matter Phenomenon](extra/oph_dark_matter_paper.pdf)**: dark-matter phenomenology and MOND-like galaxy limit.
- **[Theoretical Bounds on chi-nu in Observer-Patch Holography](extra/chi_nu_susceptibility_bounds.pdf)**: conditional quotient-edge band `0.9343006394893864 <= chi_nu^can <= 1`; uniform-branch exact value `exp(-P/24)`; engineering chart values scale as `N_coh^-1`.
- **[Thinking as Patch-Net Fixed-Point Search](extra/thinking_as_patch_net_fixed_point_search.pdf)**: cognition and qualia as recurrent patch consensus.
## More
- **Website:** [floatingpragma.io/oph](https://floatingpragma.io/oph)
- **Theory explainer:** [floatingpragma.io/oph/theory-of-everything](https://floatingpragma.io/oph/theory-of-everything)
- **Simulation-theory explainer:** [floatingpragma.io/oph/simulation-theory](https://floatingpragma.io/oph/simulation-theory/)
- **Coherence map:** [coherence.floatingpragma.io](https://coherence.floatingpragma.io): public graph surface for OPH concepts, overlaps, and cross-domain routes.
- **Applications:** [omega.floatingpragma.io](https://omega.floatingpragma.io): public applications page for OPH hardware, compute, energy, AGI, lift, and optical chamber consensus.
- **Three-body OPH demo:** [3body.floatingpragma.io](https://3body.floatingpragma.io): an extra simulator and proof walk-through for the OPH finite patch-net formulation of the three-body problem, framed as a loop-holonomy gluing example. No closed-form elementary solution is claimed.
- **Blog:** [blog.floatingpragma.io](https://blog.floatingpragma.io/) collects public OPH essays. Start with [Semiotics and the Physics of Meaning](https://blog.floatingpragma.io/semiotics-and-the-physics-of-meaning), [The Trigger](https://blog.floatingpragma.io/the-trigger), and [P = NP on the Observer Screen](https://blog.floatingpragma.io/p-equals-np-on-the-observer-screen). The computation essay treats `P = NP` as an observer-screen slogan, not a claim to solve the classical complexity problem.
- **Book:** [oph-book.floatingpragma.io](https://oph-book.floatingpragma.io)
- **Guided study app:** [learn.floatingpragma.io](https://learn.floatingpragma.io/)
- **Questions and detailed explanations:** OPH Sage on [Telegram](https://t.me/HoloObserverBot), [X](https://x.com/OphSage), or [Bluesky](https://bsky.app/profile/ophsage.bsky.social)
- **OPH Notebook:** [NotebookLM source notebook](https://notebooklm.google.com/notebook/d5249760-6ce8-44a0-927b-ccf90402711a) with explainer videos and additional study material.
- **Lab:** [oph-lab.floatingpragma.io](https://oph-lab.floatingpragma.io)
- **Common objections:** [extra/COMMON_OBJECTIONS.md](extra/COMMON_OBJECTIONS.md)
- **IBM Quantum note:** [extra/IBM_QUANTUM_CLOUD.md](extra/IBM_QUANTUM_CLOUD.md)
## Status Table
The fine-structure display row uses the fixed-point value
$\alpha^{-1}(0)=137.035999177(21)$ and
$P\simeq1.6309682094$. The source-side audit and endpoint residual records
live in the particle paper, where they are kept separate from the public
fixed-point row.
The weak-boson pair is a validation row. Charged-lepton absolute masses are
target-anchored witness rows. The auxiliary direct-top average is a validation
row. Hadron-controlled rows use the policy in [`HADRON.md`](HADRON.md):
source-only OPH values stay separate from OPH plus empirical hadron closure
values carried by the empirical $e^+e^-\to\mathrm{hadrons}$ payload class.
Strong CP is work in progress in the selected-class quark theorem:
the available corpus does not derive the QCD theta angle, does not emit the
physical strong-CP angle, and does not prove that the physical strong-CP phase
vanishes. The required bridge is the phase, anomaly, and topological-angle
descent on the realized branch.
## Repository Guide
- **[`paper/`](paper):** PDFs, LaTeX sources, and release metadata.
- **[`APPLICATIONS.md`](APPLICATIONS.md):** high-level application map for
OPH energy, compute, AGI, and local-lift use cases.
- **[`book/`](book):** OPH Book source and generated downloadable PDF. Print-PDF build notes live in [`book/README.md`](book/README.md).
- **[`code/`](code):** computational material, particle outputs, and experiments.
- **[`HADRON.md`](HADRON.md):** policy for QCD-limited particle rows, empirical
$e^+e^-\to\mathrm{hadrons}$ input, and fine-structure hadron closure.
- **[`assets/`](assets):** public diagrams and figures.
- **[`extra/`](extra):** maintained public notes such as objections, experimental write-ups, and selected supporting essays.
## OPH and the Sciences
A domain -> subdomain -> OPH-area map spanning mathematics, computer science, information and inference, complex systems, theoretical physics, quantum information, and measurement foundations. Click to open the full poster PNG.
## License And Patent Policy
The authored material in this repository is licensed under
[CC BY-NC-SA 4.0](LICENSE), with the repository-wide
[OPH Open Use And Anti-Patent Covenant](PATENTS.md) applying to OPH-derived
ideas, implementations, devices, methods, applications, software, simulations,
and hardware designs.
In short: OPH is published so the mathematics, software, applications, devices,
hardware designs, simulations, engineering methods, and experimental
implementations can be studied, tested, implemented, modified, deployed,
manufactured, and shared. OPH-derived work may not be used to create private
patent monopolies or patent claims that restrict others from practicing OPH.
See [PATENTS.md](PATENTS.md) for the canonical policy text and copy/paste
website notices.
