Quantum Collapse

Shared-State Constraint Collapse (SSCC)
A frozen architecture for sparse global recovery of discrete configurations

Author: Logan Voss
github.com/LoganVoss/Quantum-Collapse

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Overview

Quantum Collapse (scientific designation: Shared-State Constraint Collapse, SSCC) recovers a global discrete configuration from sparse observations when hidden variables are shared across positions.

Where ordinary accounting treats each observation as local information, SSCC treats the topology of shared latent labels as part of the information budget. A measurement at one index can force symbols at co-labeled indices, project a finite residual hypothesis class, and—when structural prerequisites hold—identify a unique global state. When shared topology is removed, unique nonlocal recovery is expected to fail.

Field	Value
Algorithm name	Quantum Collapse
Scientific name	Shared-State Constraint Collapse (SSCC)
Author	Logan Voss
Methods status	Manuscript complete; computational validation green
Theory status	Prospective signal; not claimed as a completed law
Core fingerprint	32945117a118e4277b05c567b27ae367a341b7afcd0cdae6cd81005d4b1b8b4e

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Contents

1. Motivation
2. Mathematical model
3. Algorithm
4. Prerequisites
5. Principal results
6. Claim structure
7. Publications
8. Repository layout
9. Quick start
10. Reproducibility
11. Citation

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1. Motivation

Sparse observations of a discrete configuration often appear underdetermined. If every coordinate has an independent latent state, local measurements typically cannot determine the global target. If coordinates share latent labels, fixing a shared latent at one measured site constrains every co-labeled site.

A measurement may therefore contribute both local and topological information:

$$ I_{\mathrm{total}} = I_{\mathrm{local}} + I_{\mathrm{topological}} $$

This repository makes that separation operational: formal prerequisites, a theorem program, sealed evaluation protocols, topology ablations, capacity controls, and multi-implementation agreement.

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2. Mathematical model

2.1 Transport law

For positions $i \in {0,\ldots,n-1}$ over alphabet $\mathbb{Z}/m\mathbb{Z}$:

$$ C_i \equiv P_i + a_i + g(\kappa_i) + \gamma_i \pmod{m} $$

$$ P_i \equiv C_i - a_i - g(\kappa_i) - \gamma_i \pmod{m} $$

Symbol	Role	Known at recovery?
$C_i$	Observation	Yes
$a_i$, $\gamma_i$	Public local geometry (or escrowed card)	Yes
$\kappa_i$	Shared-label topology	Yes
$g(\kappa)$	Latent shared state	Inferred from measurements
$P_i$	Target symbol	Only on sparse set $M$
$\mathcal{H}$	Finite residual hypothesis class	Frozen before recovery

2.2 Entanglement gain

Let $\Pi_M(\mathcal{H})$ be the residual hypotheses consistent with the measurement-induced mask and a globally consistent $g$:

$$ E(M) = \log_2 \lvert \mathcal{H} \rvert - \log_2 \lvert \Pi_M(\mathcal{H}) \rvert $$

Against an injective-label control $G_{\mathrm{inj}}$ (no shared multiplicity):

$$ E_{\mathrm{nonlocal}}^{\mathrm{op}}(M) = E_{G_\kappa}(M) - E_{G_{\mathrm{inj}}}(M) $$

This is a classical accounting quantity for shared-state discrete systems.

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3. Algorithm

3.1 Pipeline

measure sparse anchors
  → infer shared states g(κ)
  → propagate nonlocal mask
  → project finite residual class ℋ
  → collapse (deterministic ranking + tie-break)
  → verify inverse re-encryption

Hard structural projection precedes soft ranking. Domain scores do not invent candidates; they only order survivors of $\Pi_M(\mathcal{H})$.

3.2 Reference implementations

Component	Path
Reference engine	qc_core/
Formal specification	synthesis/phase0/SPECIFICATION.md
Independent Python SPEC port	novelty_proof/independent_impl/
Factor-graph / SAT-style solvers	validation/solvers/
JavaScript SPEC port	synthesis/phase4_solvers/qc_collapse.js

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4. Prerequisites

ID	Requirement
P1	Finite alphabet $m \ge 2$ and length $n \ge 1$
P2	Shared-label map $\kappa$ with multiplicity
P3	Local law invertible in $P_i$ once $g(\kappa_i)$ is known
P4	Sparse measurements $M$
P5	Finite residual class $\mathcal{H}$, committed before recovery
P6	Frozen ranking rule and deterministic tie-break

If shared topology is removed (injective $\kappa$), unique nonlocal recovery is expected to fail. That outcome is treated as correct under the model.

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5. Principal results

Figures are drawn from sealed machine certificates in this repository.

5.1 Topology-dependent recoverability

Control	Unique-recovery rate (representative suites)
Shared labels	~100%
Injective labels	~0–5% at low measurement density; ~32% at $n_c = 2$ in the phase campaign

5.2 Residual-class compression

Structured residual-class instance ($n = 32$, five measurements):

Method	Outcome
Local constraints only	1,440 residual survivors
Domain ranking only	True state at rank 41,865
SSCC / Quantum Collapse	Exact recovery; $\lvert H_{\mathrm{cons}} \rvert = 1$

Compression under shared-state projection: 1,440 → 1.

5.3 Role-separated Internal–External audit

Authority, builder, and evaluator are path-separated. Contamination scan: clean.

Class	Result
Suitable shared-state challenges	3 / 3 exact unique recoveries
Unsuitable injective challenge	1 / 1 correct non-unique reject ($\lvert H_{\mathrm{cons}} \rvert = 1920$)

Operational nonlocal gains on suitable sealed events were approximately 3.6–11.9 bits, with substantial non-measurement forced symbols when topology was intact.

5.4 Multi-implementation agreement

Recovery agrees across the reference engine, independent SPEC Python, hard factor-graph style, SAT unit-propagation style, and a JavaScript SPEC port.

5.5 Noise detectability

In tested shared-key ensembles, zero corrupted measurements yield exact recovery; a single incompatible corruption yields conflict / empty recovery rather than silent wrong unique collapse.

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6. Claim structure

Level	Meaning	Status
N1	Formal recovery architecture	Established
N2	Prospective withheld prediction under freeze	Established
N3	Foreign-domain transfer and independent implementation	Established
N4	Multi-challenge seal-before-reveal	Established computationally; multi-institution execution pending
N5	General recoverability law	Prospective signal only

Layering

1. Established — architecture, seals, ablations, multi-implementation agreement
2. Conditional — historical applications depend on declared card and residual-class assumptions
3. Prospective — transferable critical-density law $\rho_c = F(\ldots)$, pending external ensembles

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7. Publications

Publication	Path	Description
Methods	docs/papers/METHODS.md	Full methods manuscript: architecture, theorems, worked example, quantitative evaluation
Theory	docs/papers/THEORY.md	Prospective recoverability program and entanglement-gain definitions; not submitted as a completed law

Supporting reports:

Document	Path
Internal–External audit	docs/audits/IE-AUDIT-RESULTS.md
Program completion summary	docs/excellence/PROGRAM_COMPLETION.md
Novelty program narrative	docs/novelty/NOVELTY_PROOF_N1_N5.md

The Methods publication is the present contribution. The Theory publication remains provisional until independent phase-boundary experiments are generated externally.

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8. Repository layout

Quantum-Collapse/
├── README.md
├── FOLDER_INDEX.md
├── qc_core/                 Reference SSCC engine
├── validation/              Role-separated Internal–External audit
├── synthesis/               Program synthesis, publications package, external handoff
├── novelty_proof/           N1–N5 proof machinery
├── n2_machine/ · ports/     Prospective N2 · foreign N3 adapters
├── verification_kernel/     Historical verification path
├── challenges/              Sealed challenge packages
├── docs/
│   ├── papers/              Methods · Theory
│   ├── audits/              IE audit report
│   ├── assets/              Figures
│   ├── excellence/ · novelty/ · verification/
│   └── archive/             Older materials
├── outputs/                 Machine certificates
└── Archive/                 Pre-modern laboratory archive

Large regenerable hypothesis enumerations (HYPOTHESES.json) are gitignored and rebuilt by challenge generators when needed.

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9. Quick start

Requirements: Python 3.10+. Optional: Node.js for the JavaScript port.

git clone https://github.com/LoganVoss/Quantum-Collapse.git
cd Quantum-Collapse

# Role-separated Internal–External audit
python3 validation/run_internal_external.py

# Full program synthesis board
python3 synthesis/run_synthesis.py

# Prospective N2 and foreign N3 machines
python3 run_n2_n3.py

# Optional: JavaScript SPEC port
node synthesis/phase4_solvers/qc_collapse.js

External handoff materials (authority / builder / evaluator):

synthesis/external_handoff/

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10. Reproducibility

Item	Location
Core fingerprint	qc_core/; synthesis/phase0/FROZEN_CORE.sha256
Glass-box seal	synthesis/phase0/GLASS_BOX_MANIFEST.json
Claim-to-artifact ledger	synthesis/phase0/CLAIM_TO_ARTIFACT_LEDGER.md
IX machine verdict	validation/outputs/IX_VERDICT.json
Program completion board	synthesis/outputs/PROGRAM_COMPLETION_BOARD.json

Expected core fingerprint:

32945117a118e4277b05c567b27ae367a341b7afcd0cdae6cd81005d4b1b8b4e

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11. Citation

Voss, L. Shared-State Constraint Collapse (Quantum Collapse). Computational research package and methods manuscript, 2026.
https://github.com/LoganVoss/Quantum-Collapse

Prefer the scientific name Shared-State Constraint Collapse (SSCC) in academic prose. Cite Methods for architecture and validation; cite Theory only as a prospective note until external gates are met.

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_{Logan Voss · Quantum Collapse · Shared-State Constraint Collapse}