---
title: "PAPER_1976 — HUDF I_0 = 0.05 EXACT and τ_inter = SO_5^9 = 1 Gyr Are Confirmations of Already-Listed PAPER_265 (Dual-Channel Cascade) and PAPER_1952 (Slot-9 Galaxy-Quenching Timescale) Predictions — Explicit Retraction of Round 111's Initial 'Novel Intra-System Twin Identity + Slot-9 Extension' Framing, Which Missed That Both Findings Were Predicted Rows in Existing Catalogs"
author: "Daniel T. Murphy"
date: "2026-07-09"
tags: [HUDF, I_0, F_TRZ_over_2, tau_inter, SO_5_9, PAPER_265, PAPER_1952, PAPER_1955, PAPER_1949, honest-scholarship, retraction]
draft: 3
status: draft-3
---

# PAPER_1976 — HUDF I_0 and τ_inter Confirmations

## Abstract

**Round 111 double-check** initially proposed authoring PAPER_1976 as documentation of:
- (A) "Novel HUDF intra-system twin identity `I_0 = F_TRZ/2 = 0.05 EXACT`" appearing in both `HUDFBaseGravityCalculator` (Round 109) and `HUDFGalaxyInteractionCalculator` (Round 111)
- (B) "Novel `τ_inter = SO_5^9 = 1 Gyr` cosmological slot-9 extension of PAPER_1955's SO_5-power galactic ladder"

**Prior-art check surfaced two critical corrections**:

1. **PAPER_265 ("HUDF Dual-Channel Interaction Cascade Buoyancy — Quadratic I(t) Amplification at Cosmic Merger Peak", March 2026)** documents `I_0 = 0.05` as the canonical HUDF peak interaction factor. PAPER_265's uniquely rare discovery is that this I(t) is applied to TWO channels simultaneously (base MUGE + UQFF unification), producing quadratic buoyancy amplification `(1 + I_0)²` at cosmic merger peak. **The "intra-system twin identity" I noted in Round 111 is PAPER_265's already-documented dual-channel cascade — NOT a new twin discovery.**

2. **PAPER_1952 ("Galaxy-Scale SO_5-Power Timescale Hierarchy")** explicitly lists `SO_5^9 = 1 Gyr` as a **predicted candidate slot** with hypothesized physical interpretation "galaxy quenching timescale" (referencing Peng 2010 star-formation cessation ~1 Gyr for massive galaxies). PAPER_1952 Section 4.2 states:
   > *"If the SO_5^9 = 10⁹ yr slot corresponds to universal galaxy-quenching timescale, systematic surveys of quenched-galaxy age distributions should show clustering at 1 Gyr."*
   
   PAPER_1955 further lists "SO_5^9 to SO_5^10 | Cosmological timescales | (candidate future)" in its ladder table. **The "slot-9 extension" I noted in Round 111 is confirmation of PAPER_1952's already-listed candidate prediction — NOT a novel ladder extension.**

3. **The F_TRZ/2 multiplier form is not novel** — PAPER_1966 documents it as an "Archimedean half-coefficient" in the β_4 = (D_phys-1)·F_TRZ/2 = 3/20 identity (PAPER_1165 companion triangular normalization). PAPER_1478, PAPER_1861, and PAPER_1891 also use F_TRZ/2 in various contexts.

**Positioning (honest scope after prior-art check).** This paper contributes:

1. **Confirmation** of PAPER_265's dual-channel cascade at Round 111 via corpus-audit finding that `HUDFBaseGravityCalculator` and `HUDFGalaxyInteractionCalculator` both use `I_0 = 0.05` (the two channels PAPER_265 describes).
2. **Empirical confirmation** of PAPER_1952's SO_5^9 = 1 Gyr candidate prediction: `HUDFGalaxyInteractionCalculator` uses `τ_inter = 1 Gyr` as the interaction timescale, matching PAPER_1952's prediction.
3. **Explicit retraction of Round 111's initial "novel intra-system twin + slot-9 extension" framing**, replaced with the correct "confirmation of PAPER_265 and PAPER_1952 already-listed predictions" interpretation.

The paper does NOT contribute:
- The HUDF I_0 = 0.05 dual-channel cascade (PAPER_265 seminal).
- The SO_5^9 = 1 Gyr slot prediction (PAPER_1952 seminal).
- The F_TRZ/2 = 0.05 multiplier form (PAPER_1966 Archimedean half-coefficient seminal).
- The (D_phys-1)·F_TRZ/2 = 0.15 β_4 relation (PAPER_1165 triangular ladder seminal).

Independent-primitive count remains **8** (PAPER_1521 + PAPER_1522 + PAPER_1960 landmark trio). No new primitives.

## 1. PAPER_265's Dual-Channel Cascade — Prior Art for I_0 = 0.05

**PAPER_265 ("HUDF Dual-Channel Interaction Cascade Buoyancy — Quadratic I(t) Amplification at Cosmic Merger Peak", March 2026, session 72g)** documents:

- **Canonical value**: `I_0 = 0.05` (Peak interaction factor at z → 3.5)
- **Dual-channel structure**: I(t) = I_0 · exp(-t/τ_inter) is applied to BOTH the base MUGE term (term1) AND the UQFF unification term (term2) — same modulation `(1 + I(t))` on both channels
- **Quadratic amplification**: `(1 + I(t))²` net enhancement at cosmic merger peak (t → 0 corresponds to z → 3.5, coinciding with HUDF observational epoch)
- **Cascade excess**: `Δ_cascade = I_0² · U_g1 · (1 + f_TRZ)` at peak; the (1+I_0)² factor arises because both channels contribute
- **Uniquely rare discovery status**: PAPER_265's classification is "Uniquely rare discovery — dual-channel interaction cascade absent from all prior UQFF modules"
- **Falsifiability tests**: HST/JWST merger pair fractions at z ~ 3-4 should show anomalously enhanced tidal bridge luminosity proportional to I_0²; ALMA Band 3 CO observations should show velocity dispersion ∝ (1 + I_0)² relative to isolated galaxies

**Corpus-audit finding (this paper)**: The `HUDFBaseGravityCalculator` (Round 109 upgrade) and `HUDFGalaxyInteractionCalculator` (Round 111 upgrade) both use `I_0 = 0.05` as the canonical interaction amplitude. These two calculators represent PAPER_265's "two channels" (base + interaction) — the "intra-system twin identity" is thus **PAPER_265's already-published dual-channel cascade structure**, verified at the code-attribution level by having I_0 appear in both stubs.

## 2. PAPER_1952's SO_5^9 = 1 Gyr Candidate — Prior Art for τ_inter Attribution

**PAPER_1952 ("Galaxy-Scale SO_5-Power Timescale Hierarchy — PDR Erosion = Nuclear Starburst t_ff = 5 Myr = (SO_5/2) · SO_5^6 EXACT + Extended SO_5^n Grid")** documents the full SO_5-power ladder including candidate slots:

| SO_5 slot | Timescale | Physical interpretation | Status |
|---|---|---|---|
| SO_5^6 = 1 Myr | Pillars PDR erosion | PDR photoevaporation | Populated (PAPER_435, PAPER_1948) |
| (SO_5/2)·SO_5^6 = 5 Myr | Horsehead PDR + NGC 4945 nuclear SB | Triple closure | Populated (PAPER_1948, PAPER_1952) |
| D_phys·SO_5^6 = 4 Myr | Bubble PDR erosion | PDR photoevaporation | Populated (PAPER_440, PAPER_1948) |
| SO_5^7 = 10 Myr | AGN duty cycle candidate | Systematic AGN feedback survey | Candidate (Round 80) |
| SO_5^8 = 100 Myr | Galaxy SF cycle | StarFormationGravity model | Populated (PAPER_1952) |
| A_5·SO_5^8 = 6 Gyr | Nuclear star cluster relaxation? | Candidate | (PAPER_1946) |
| **SO_5^9 = 1 Gyr** | **Galaxy quenching timescale?** | **Candidate — Peng 2010 anchor** | **Candidate empty slot** |
| SO_5^10 = 10 Gyr | Hubble time | Cosmological | Empty |

PAPER_1952 Section 4.2 (Prediction: SO_5^9 = 1 Gyr):

> *"Candidate application: galaxy quenching. Star formation cessation in massive galaxies occurs on ~1 Gyr timescales (Peng 2010, etc.). If the SO_5^9 = 10⁹ yr slot corresponds to universal galaxy-quenching timescale, systematic surveys of quenched-galaxy age distributions should show clustering at 1 Gyr."*

PAPER_1955 further echoes this in its ladder table: "SO_5^9 to SO_5^10 | Cosmological timescales | (candidate future)".

**Round 111 empirical confirmation**: `HUDFGalaxyInteractionCalculator` uses `τ_inter = 3.156×10¹⁶ s = 1 Gyr` as the canonical HUDF galaxy-interaction timescale. This value:
- Matches PAPER_1952's `SO_5^9 = 1 Gyr` candidate slot **exactly**
- Applies at cosmic merger epoch (z → 3.5) which coincides with HUDF observational peak (PAPER_265)
- Physical interpretation "cosmic merger interaction timescale" is closely related to PAPER_1952's "galaxy quenching timescale" (both are ~Gyr-scale galaxy-scale evolutionary timescales)

The Round 111 attribution `τ_inter = SO_5^9 = 1 Gyr` is thus **confirmation of PAPER_1952's already-listed candidate prediction**, not a new slot-9 extension.

## 3. Round 111's Initial Framing Was Incorrect — Retraction

The Round 111 summary initially proposed:

> *"PAPER_1976 authoring (I_0 = F_TRZ/2 HUDF intra-system twin + τ_inter = SO_5^9 = 1 Gyr cosmological slot-9 confirmation is the strongest new candidate — extends PAPER_1955 ladder + adds novel PAPER_1960 F_TRZ/2 intra-system attribution)"*

**Both claims were incorrect on prior-art check**:

1. **"Novel HUDF intra-system twin"** is retracted. The twin structure is PAPER_265's already-documented dual-channel cascade. The two HUDF stubs (`HUDFBaseGravityCalculator` and `HUDFGalaxyInteractionCalculator`) represent PAPER_265's two channels (base MUGE + UQFF unification), and both using `I_0 = 0.05` is the code-level reflection of PAPER_265's structural observation.

2. **"Novel slot-9 extension of PAPER_1955 ladder"** is retracted. PAPER_1952 explicitly lists `SO_5^9 = 1 Gyr` as a candidate slot with predicted physical interpretation "galaxy quenching timescale" (Peng 2010). PAPER_1955 also lists SO_5^9-SO_5^10 as candidate cosmological timescales.

3. **"Novel PAPER_1960 F_TRZ/2 intra-system attribution"** is retracted. PAPER_1966 documents F_TRZ/2 as an "Archimedean half-coefficient" (β_4 = (D_phys-1)·F_TRZ/2 = 0.15 EXACT). The 0.05 = F_TRZ/2 = 1/(2·SO_5) multiplier form is a component of the well-established β_i triangular ladder from PAPER_1165 (session 252, 2026-05-10).

The corrected framing: **this paper is a Round-attribution confirmation of two already-published catalog predictions** (PAPER_265's dual-channel cascade + PAPER_1952's SO_5^9 = 1 Gyr slot). It is analogous to:
- PAPER_1968 (MW v_flat confirming PAPER_1906's Galactic-scale row)
- PAPER_1970 (Virgo r_c confirming PAPER_1918's 40-kpc catalog row)
- PAPER_1973 (Horsehead g confirming PAPER_1906's Nebular-scale assertion)
- PAPER_1972 / 1974 / 1975 (Round-misidentification correction papers)

## 4. What Round 111 Does Confirm

Despite the retraction of the "novel" framings, Round 111's HUDF stub upgrades have three modest positive contributions:

1. **Empirical confirmation of PAPER_265's dual-channel cascade at code-attribution level**: both HUDF calculators use `I_0 = 0.05` as expected by PAPER_265's dual-channel structure.

2. **Empirical confirmation of PAPER_1952's SO_5^9 = 1 Gyr candidate slot**: `HUDFGalaxyInteractionCalculator` uses `τ_inter = 1 Gyr` matching the SO_5^9 slot exactly. This does not itself prove PAPER_1952's "galaxy quenching timescale" physical interpretation, but confirms that UQFF stub-level canonical parameters use the SO_5^9 value at the HUDF cosmological-merger epoch.

3. **Corpus-audit finding**: The HUDF stub family systematically uses PAPER_265's canonical parameter set (I_0 = 0.05, τ_inter = 1 Gyr, M_0 = 10¹² M_sun = SO_5^12, etc.) as its default. This confirms integrated design between PAPER_265's dual-channel theory and the CondensedPhysics stub implementations.

## 5. PAPER_1918 / PAPER_1949 / PAPER_1955 Framework Consistency

The corrected framing aligns with three broader UQFF frameworks:

- **PAPER_1918 (Phase 3 Comprehensive Inventory)**: Multi-context integer identity meta-framework. HUDF I_0 = 0.05 is one such multi-context observation.
- **PAPER_1949 (F_TRZ Three-Face Framework)**: Face 1 (amplitude) 10-instance grid documents F_TRZ across multiple UQFF contexts. HUDF I_0 = F_TRZ/2 is not a Face-1 pure form (it's the half-multiplier), but is consistent with PAPER_1966's Archimedean-half derivation.
- **PAPER_1955 / PAPER_1952 SO_5-power ladder**: `τ_inter(HUDF) = SO_5^9 = 1 Gyr` fills the previously-empty slot-9 as specifically predicted for galaxy-scale evolutionary timescales.

Round-attribution instances of Round 111 at HUDF are thus specific-application instances of already-documented general frameworks, not new discoveries.

## 6. Prior Art — What This Paper Does NOT Claim

### 6.1 I_0 = 0.05 dual-channel HUDF cascade is not new

**PAPER_265 seminal.** Full "uniquely rare discovery" status; quadratic amplification (1 + I_0)²; falsifiability tests via HST/JWST + ALMA.

### 6.2 τ_inter = SO_5^9 = 1 Gyr is not new

**PAPER_1952 seminal.** Explicit candidate slot with predicted physical interpretation (galaxy quenching timescale, Peng 2010 anchor). PAPER_1955 companion.

### 6.3 F_TRZ/2 = 0.05 Archimedean half-coefficient is not new

**PAPER_1966 seminal** for the (D_phys-1)·F_TRZ/2 = 3/20 = 0.15 β_4 identity form + PAPER_1165 triangular ladder companion.

### 6.4 What this paper contributes (narrow)

1. **Corpus-audit confirmation** that HUDF stub family uses PAPER_265's canonical dual-channel parameter set at code-attribution level.
2. **Empirical confirmation** that `τ_inter = SO_5^9 = 1 Gyr` matches PAPER_1952's candidate slot-9 prediction.
3. **Explicit retraction** of Round 111's initial "novel intra-system twin + slot-9 extension" framing, replaced with "confirmation of existing catalog predictions" interpretation.

The paper is a narrow attribution + retraction + code-level confirmation. Following the PAPER_1968/1970/1973 attribution-paper template + PAPER_1972/1974/1975 correction-paper template.

## 7. Cross-References

- **PAPER_265 (SEMINAL)** — HUDF Dual-Channel Interaction Cascade Buoyancy Quadratic Merger Amplification (I_0 = 0.05 canonical + dual-channel structure)
- **PAPER_1952 (SEMINAL for SO_5^9 = 1 Gyr candidate)** — Galaxy-Scale SO_5-Power Timescale Hierarchy (Section 4.2 galaxy quenching prediction)
- **PAPER_1955** — SO_5-Power Galactic Structural Ladder (companion ladder framework)
- **PAPER_231** — HUDF z=3.5 Double I(t) Modulation (PAPER_265's parent paper for HUDF dual-channel form)
- **PAPER_266** — HUDF primordial (PAPER_1906 Table 1 row 8 anchor, companion HUDF paper)
- **PAPER_444** — HUDF Galaxies-Galore per-system MUGE
- **PAPER_1966** — M_sf = 3/(2·SO_5) starburst mass fraction (F_TRZ/2 Archimedean half-coefficient prior art)
- **PAPER_1165 (session 252)** — β_i triangular buoyancy coupling ladder (triangular normalization companion)
- **PAPER_1960** — F_TRZ = 1/SO_5 landmark (source of F_TRZ derivative primitive)
- **PAPER_1949** — F_TRZ Three-Face Framework (Face-1 amplitude formalism)
- **PAPER_1918** — Multi-context integer identity meta-framework
- **PAPER_1968** — MW v_flat F_UBi_i_99 closure (attribution paper template)
- **PAPER_1970** — D_phys × SO_5 = 40 multi-scale attributions (template)
- **PAPER_1972 / 1974 / 1975** — Round-misidentification correction papers (companion templates)
- **PAPER_1521** — D_BSFG derivative landmark
- **PAPER_1522** — K_MEX derivative landmark

## 8. Limitations + Open Questions

- The corpus audit confirms that HUDF stub family uses PAPER_265's dual-channel canonical parameters, but does not itself observationally test the (1 + I_0)² amplification prediction. HST/JWST merger pair surveys at z ~ 3-4 remain the primary observational falsifiability test.
- PAPER_1952's SO_5^9 = 1 Gyr galaxy-quenching prediction is not tested by this paper — Round 111 only confirms the τ_inter = 1 Gyr canonical stub value, not the "galaxy quenching timescale" physical interpretation. Systematic quenched-galaxy age distributions (Peng 2010 follow-ups) remain the primary observational test.
- The physical distinction between "cosmic merger interaction timescale" (Round 111's τ_inter interpretation) and "galaxy quenching timescale" (PAPER_1952's SO_5^9 interpretation) is worth examining. Both are ~Gyr scale galaxy-evolution timescales; whether they refer to the same underlying timescale or distinct-but-numerically-coincident timescales is open.
- The two HUDF stubs identified in this corpus audit (`HUDFBaseGravityCalculator` + `HUDFGalaxyInteractionCalculator`) are two of the many HUDF-related calculators in `CondensedPhysics.py`. Systematic audit of the full HUDF stub family for consistent PAPER_265 parameter usage across all stubs is a candidate future task.

## 9. Revision Log

**Draft 1 (2026-07-09):** Initial write. Round 111 double-check initially proposed "novel intra-system twin + slot-9 extension" framing. Prior-art check surfaced:

- PAPER_265 seminal for HUDF dual-channel cascade (I_0 = 0.05 canonical + quadratic amplification)
- PAPER_1952 seminal for SO_5^9 = 1 Gyr candidate slot prediction (Section 4.2 galaxy quenching)
- PAPER_1955 companion listing SO_5^9-SO_5^10 as candidate cosmological timescales
- PAPER_1966 seminal for F_TRZ/2 Archimedean half-coefficient form

Draft 1 is written from the corrected framing: this paper is a narrow attribution + retraction paper confirming already-listed catalog predictions from PAPER_265 and PAPER_1952. Both Round 111 "novel" framings (intra-system twin + slot-9 extension) are retracted.

Following the PAPER_1972 / 1974 / 1975 Round-misidentification correction template, Draft 1 is positioned narrowly from the start with the double retraction as the substantive content.

Reader takeaway: this paper is the fourth consecutive Round-attribution correction paper in this session (PAPER_1972 v_wind Antennae + PAPER_1974 R_star stub-default + PAPER_1975 Q_UQFF three-path retraction + this paper's HUDF twin+slot-9 retraction). Each documents Round findings that appeared novel initially but on prior-art check were confirmed as instances of already-documented general frameworks. The corrective discipline continues to stabilize the corpus's semantic integrity.

**Drafts 2/3 (2026-07-09):** Verified via targeted searches for PAPER_265 (confirmed dual-channel cascade uniquely rare discovery status + I_0 = 0.05 canonical + quadratic (1+I_0)² amplification), PAPER_1952 (confirmed SO_5^9 = 1 Gyr candidate slot + Peng 2010 galaxy quenching anchor), PAPER_1955 (confirmed SO_5^9-SO_5^10 candidate cosmological range), PAPER_1966 (confirmed F_TRZ/2 Archimedean half-coefficient documentation), and PAPER_1165 (confirmed triangular ladder session 252 seminal). No further prior-art corrections needed beyond Draft 1's double-retraction framing.

**Meta-observation for the session**: This is the ninth consecutive paper (PAPER_1968→1976) with Draft 1 narrow from the start following the honest-scholarship stabilization pattern. Four of these nine (PAPER_1972, 1974, 1975, 1976) are explicit Round-misidentification correction papers. The pattern suggests that as the corpus matures, "novel" findings from Round double-checks increasingly turn out to be confirmations of already-documented general frameworks — an expected outcome as the framework's coverage density approaches saturation. The correction papers themselves have documentary value: they attribute specific Round instances to their seminal papers and prevent overclaim propagation into future work.

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**License:** AGPL-3.0 (see LICENSE); Commercial license option per COMMERCIAL.md.
**Copyright:** © 2025-2026 Daniel T. Murphy / Star-Magic Research Program.
