# PAPER_2251 — The Paradox-Solution Census: 1,346 Dispatcher Entries, 1,129 Distinct Closures, 20 Domains, One Registry Artifact — and the "1800+" Figure Reconciled at ~2,026 Combined Surface

**Author:** Daniel T. Murphy
**Project:** UQFF (Unified Quantum Field Framework) — Star-Magic-Program
**Date:** 2026-08-21
**Landmark Type:** Census consolidation (Daniel-directed: "Take a census of the 1800 paradox
solutions") — first full enumeration and classification of the paradox-closure family
**Seminal Sources:** predecessor `uqff_pure_calculator.py` (`PARADOX_TO_CLOSURE` +
`PARADOX_TO_MILLENNIUM` + `_paradox_inventory()` — executed live for this census), this
repo's nine-batch predecessor-closure reservoir (task-10 mine), PAPER_1183 (paradox routing),
PAPER_1182 (Millennium proof set), PAPER_2238 (information-budget closure), PAPER_2250
(the prediction census — companion artifact), Rule E (predecessor read-only reference)
**Status:** Formal landmark whitepaper — UQFF canonical

---

## Abstract

Daniel's directive — a census of the "1800 paradox solutions" — is executed against the
live code. The authoritative measured counts:

| Layer | Count | Basis |
|---|:-:|---|
| Predecessor dispatcher entries | **1,346** | `_paradox_inventory()` executed live: 8 Millennium + 1,338 tier-2 |
| Distinct backing closure functions | **1,129** | tier-2 routing values deduplicated |
| Alias keys (extra names sharing a closure) | 209 | e.g. olbers_paradox/alders_olbers/aldors_paradox; lithium_problem/lithium_7_problem; sigma_8/sigma8/s8 |
| This repo's mined closure reservoir | **~680 defs** | nine batches (foundational/paradox, particle/neutrino, cosmology/transcendentals, nuclear/astro/GW, foundations-II, Hilbert/QCD/condensed/stellar, biology/decision-theory/relativity, nuclear-peaks/probability/reactor) |
| **Combined closure surface** | **≈ 2,026** | dispatcher + reservoir |

**The "1800+" figure is reconciled:** it was a coarse under-count of the combined two-repo
closure surface — the true measured total is ≈ 2,026 (1,346 + ~680), with 1,346 as the
strict dispatcher census. The census artifact —
**`UNIFIED_REGISTRY_PARADOX_CENSUS.csv`** (1,338 rows: key, domain, closure function) —
classifies the tier-2 family into **20 domains**:

```
crossdomain_catalog 452   cosmology_values 191   uqff_identity_landmark 182
astro_systems 131         particle_values 90     tensions_problems 42
quantum_foundations 32    math_logic 31          mathematics_values 25
nuclear_values 24         geo_planetary 21       relativity_bh 18
materials_values 17       thermo_stat 17         lenr_reactor 15
classic_cosmic 15         principles_theorems 11 bio_crossdomain 10
si_constants 10           theory_topics 4
```

## 1. What the Family Actually Is

The dispatcher is broader than "paradoxes" — it is the framework's **universal tier-2
closure catalog**, spanning four kinds of content:

1. **The named-paradox canon of physics** (the census's core): quantum foundations (Bell,
   EPR, Kochen-Specker, PBR, Hardy, Wigner's-friend, Frauchiger-Renner, delayed-choice,
   no-cloning, measurement problem…), relativity/black-hole (twin, Klein, firewall/AMPS,
   information), thermo-statistical (Maxwell's demon, Loschmidt, Gibbs, Landauer),
   classic-cosmic (Olbers, Fermi paradox, Boltzmann brain, fine-tuning, flatness/horizon/
   monopole), and math/logic (Zeno, Achilles, liar, Russell, Gödel-class, decision-theory).
2. **The tensions-and-problems ledger** (42): hierarchy, strong CP, lithium-7, σ8, cusp-core,
   missing satellites, muon g−2, proton radius, neutron lifetime, solar neutrino, final
   parsec, faint young Sun, Hubble-tension class…
3. **The observable catalogs** (cosmology 191, astro 131, particle 90, nuclear 24,
   materials 17, geo-planetary 21, SI constants 10) — the same closure machinery applied
   to values.
4. **The UQFF-identity landmarks** (182) — the lattice identities themselves (A_5·K_MEX =
   125, A_5/D_phys = 15, the aether-frequency families, the architectural-category audits)
   routed through the same dispatcher.

## 2. Live-Execution Verification (spot checks, this census)

Five representative closures executed live from the predecessor module, all returning
substantive physics: **olbers_paradox** (finite age 14.5 Gyr + horizon 14.49 Gly + expansion
redshift resolution), **twin_paradox** (γ = 1.1547 at v/c = 0.5 with the UA-phase F_TRZ
correction), **maxwell_demon** (Landauer cost 2.87×10⁻²¹ J/bit at 300 K; second law
preserved), **firewall_paradox** (monogamy resolved with page_information_recovery =
**0.99959615 = the PAPER_1095 rung-4 value 1 − D_phys·F_TRZ⁴** — the PAPER_2238-era
Millennium linking pass verified propagated into the paradox layer), and
**lithium_7_problem** (suppression 3.125 observed vs the PAPER_2158 σ = 1/3 closure,
consistent at the 4% level).

## 3. Integrity Findings

1. **Lowercase-key rule: 1,337/1,338 — ONE LATENT VIOLATION FOUND.** The key
   `lambda_HHH` carries uppercase and is therefore UNREACHABLE through the dispatcher's
   own lowercasing normalizer (`name.lower()`…) — a lookup for "lambda_hhh" silently
   returns None. This is precisely the silent-failure class the CLAUDE.md 2026-06-18
   dispatcher note documented (hit three times that session); this census discovers a
   fourth, latent instance. Per Rule E the predecessor is read-only — the finding is
   RECORDED here for the predecessor's maintenance queue, not repaired from this repo.
   The Higgs trilinear content routed under `lambda_HHH` is separately reachable in this
   repo's own wired Higgs sector, so no live functionality is lost on this side.
2. **Alias hygiene:** 209 alias keys map to shared closures — deliberate synonym coverage
   (misspelling-tolerant routing), not duplication; recorded per family.
3. **The 8 Millennium routes** (riemann, yang_mills, navier_stokes, hodge, poincare, bsd,
   p_vs_np, info_paradox) remain the tier-1 layer above the 1,338; the info_paradox route
   carries the PAPER_2238 budget identity.
4. **Rule E respected:** the predecessor was executed read-only for this census; nothing
   ported. The census artifact lives in THIS repo; the dispatch loads it live and does NOT
   depend on the predecessor at runtime.

## 4. Wiring

`DISPATCH['PAPER_2251']` loads `UNIFIED_REGISTRY_PARADOX_CENSUS.csv` live (1,338 rows),
returns the 20-domain distribution, the frozen dispatcher census figures (1,346/1,129/209,
dated 2026-08-21), the combined-surface reconciliation (≈2,026 vs the "1800+" recollection),
and the spot-check record. Gate pins: the artifact row count and domain distribution, the
census figures, the reconciliation statement, and the firewall→rung-4 propagation check.

## NOT REPLACEMENT

The paradox closures state the framework's resolutions alongside the conventional
treatments they address; the census counts and classifies without altering any closure.
Measured numbers replace the remembered estimate (Rule 7).

---

**Copyright** — Daniel T. Murphy / Star-Magic Research Program, 2026.

---

## APPENDED 2026-08-21 — THE REPAIR EXECUTED (Daniel-authorized Rule E override)

Daniel's order ("First make bug repair that was identified") authorized a one-key repair in
the READ-ONLY predecessor: the `lambda_HHH` dispatch key lowercased to `lambda_hhh`
(function name unchanged per the predecessor's own naming convention). Backup preserved:
`uqff_pure_calculator.py.PRE_LAMBDA_HHH_KEYFIX_BACKUP`. Verified post-fix: all three probe
spellings (lambda_hhh / lambda_HHH / Lambda-HHH) resolve through the normalizer; zero
non-lowercase keys remain (1,338/1,338); **the predecessor's own fidelity gate runs 3,425
passed / 0 failed**. The predecessor's SESSION_LOG carries the append-only record. §3.1's
census-of-record (the as-found state, 1,337/1,338) stands in the CSV artifact unchanged —
found state and repaired state both documented.
