O-EMC-3 — Package Card \(\mathcal{P}_{\mathrm{EMC}}\)
Soft bulk↔face mass–energy glue · Mach \(m\) + face \(E_{\mathrm{path}}\) · not a theorem
CPT Framework — residual O-EMC · named packaging Date: 2026-08-07 Status: FROZEN v1 · package card only · join theorem remains OPEN Priors: O-EMC-1 · O-EMC-2 ·mach_absolute_me_results.md · M-PHOT · GS-B0 · Weber Meets Einstein · M3 v1.2 · absolute scale avenues (local \(a\) CLOSED-NULL)
Tags: [M] · [E process] · [E honesty] · [O] · [F]
0. One-line
\(\mathcal{P}_{\mathrm{EMC}}\) v1 is the soft bulk↔face glue: bulk/cosmological mass from the Mach absolute formula, face confinement energy \(E_{\mathrm{path}}=\hbar c/a\), seat radius fixed by \(a=\hbar/(m c)\) (optionally refined by Weber–Einstein \(\langle S\rangle\)) — a named identification package for programme language, not a derivation that independent bulk and face lengths force \(E=mc^2\).
1. Why a package card (not a theorem)
| Layer | Status after O-EMC-1/2 | |-------|------------------------| | Face energy formula \(E_{\mathrm{path}}=\hbar c/a\) | [E] under closed-path quantisation | | Absolute \(m_{\mathrm{bulk}}\) free of Compton / \(E/c^2\) | Mach supplies best candidate [M] (O-EMC-2 J2) | | Independent geometric \(a\) without \(m\) | Local absolute CLOSED-NULL | | Hard join \(E_{\mathrm{path}}\stackrel{?}{=}m c^2\) with both sides independent | OPEN / blocked without new \(L_\) |
Finding EMC3-0 [E honesty]: The only closed operational glue is identification. Naming it \(\mathcal{P}_{\mathrm{EMC}}\) prevents agents from either (i) claiming a theorem or (ii) inventing ad hoc joins.2. What is being packaged
| Symbol | Definition | Role under \(\mathcal{P}_{\mathrm{EMC}}\) | |--------|------------|------------------------------------------| | \(m_{\mathrm{Mach}}\) | Absolute electron mass from Mach formula (§3) | Bulk / cosmos mass input | | \(E_{\mathrm{path}}\) | \(\hbar c/a\) on Clifford \(T(1,1)\) (M-PHOT path energy) | Face energy | | \(a\) | Seat / \(S^3\) radius at the electron | Glue variable | | \(c\) | Face null / light speed | Exchange constant | | \(\langle S\rangle\) | Path-averaged Weber scalar (optional fine structure) | Face \(k\) refine only | | \(k_{\mathrm{EMC}}\) | \(1\) (default) or \(\langle S\rangle\) (WE variant) | Soft factor in \(E = m c^2 k\) |
Not packaged as bulk mass: face invert \(m:=E/(c^2\langle S\rangle)\); \(S^4\) free-\(A\) energy; classical \(m_{\mathrm{em}}\sim\alpha m\).3. Package axioms \(\mathcal{P}_{\mathrm{EMC}}\) (v1)
All items are adoption / programme language unless tagged otherwise.
| ID | Axiom | Tag | |----|-------|-----| | E0 | Work under M3: face ED / face Willmore / bulk mass as three books; O-WV parked | [M] architecture | | E1 | Bulk mass for the electron seat is the Mach absolute value \(m_{\mathrm{Mach}}\) | [M] · O-EMC-2 | | E2 | Face energy is path confinement \(E_{\mathrm{path}}=\hbar c/a\) on \(T(1,1)\) | [E] formula under M-PHOT package | | E3 | Soft glue (default): \(a = \hbar/(m_{\mathrm{Mach}} c)\) | [M] identification | | E4 | Under E2+E3: \(E_{\mathrm{path}} = m_{\mathrm{Mach}} c^2\) holds by construction | [E process] algebra · not bulk–face theorem | | E5 | Optional WE refine: replace E3–E4 by \(E_{\mathrm{path}} = m_{\mathrm{Mach}} c^2\,\langle S\rangle\) with \(\langle S\rangle\) from face path Weber (T(1,1), \(\varepsilon=\alpha\) ⇒ \(\langle S\rangle\approx 1-\frac34\alpha^2\)) | [M] face fine structure | | E6 | Lab CODATA \(m_e\) may be used as check, not as bulk definition under this package | [E honesty] | | E7 | Generation ratios, Willmore ladder, \(S^4\) latitude remain other books — not substituted for \(m_{\mathrm{Mach}}\) | [M] · M3 / M3-PROJ | | E8 | Hard join (independent \(a\) and \(m\), then compare) is out of scope of v1; reopen only with new \(L_\) | [O] residual |
Freeze sentence:Under \(\mathcal{P}_{\mathrm{EMC}}\) v1: \(m = m_{\mathrm{Mach}}\) (bulk); \(E = \hbar c/a\) (face); \(a = \hbar/(m c)\) (soft glue, default \(k=1\)); optional \(k=\langle S\rangle\); not a theorem that geometry forces Einstein independently on both sides.
4. Operational dictionary
4.1 Mach bulk mass (E1)
\[ \boxed{ m_{\mathrm{Mach}} = \left[ \frac{\alpha\cdot(3/8)\cdot\hbar^2\cdot H_0} {G\cdot\sqrt{6}\cdot c\cdot 6\cdot\pi^5} \right]^{1/3} } \]
| Input | Status | |-------|--------| | \(G\), \(H_0\), \(\hbar\), \(c\) | External [E] | | \(\alpha\) in formula | [M] (double-copy / not derived here) | | \(R=\sqrt{6}\,c/H_0\) | [M] anchor | | \(m_p=6\pi^5 m_e\) elimination | [E/M] baryon chain prior | | Preferred report \(H_0\) | 69 km/s/Mpc (primary); always also quote Planck / SH0ES |
| \(H_0\) | \(m_{\mathrm{Mach}}\) err vs CODATA (banked) | |--------:|---------------------------------------------:| | 67.4 | ~−0.77% | | 69.0 | ~+0.014% | | 73.0 | ~+1.9% |
4.2 Face path energy (E2)
\[ E_{\mathrm{path}} = \frac{\hbar c}{a} \quad\text{on Clifford-hosted }T(1,1). \]
4.3 Soft glue variants
| Variant ID | Glue | Equality | Use when | |------------|------|----------|----------| | \(\mathcal{P}_{\mathrm{EMC}}^{(0)}\) default | \(a=\hbar/(m_{\mathrm{Mach}} c)\) | \(E_{\mathrm{path}}=m_{\mathrm{Mach}} c^2\) | Standard programme language | | \(\mathcal{P}_{\mathrm{EMC}}^{(S)}\) WE | \(E_{\mathrm{path}}=m_{\mathrm{Mach}} c^2\langle S\rangle\) with \(\langle S\rangle\approx 1-\frac34\alpha^2\) for \(T(1,1),\varepsilon=\alpha\) | face \(k\) refine | When quoting Weber Meets Einstein with Mach mass | | Hard | independent \(a\) | compare sides | Not in v1 — needs new principle |
4.4 What each side is not
| Side | Is not | |------|--------| | \(m_{\mathrm{Mach}}\) | Face Weber invert; dual-cancel scale; hold fixed point | | \(E_{\mathrm{path}}\) | Dynamical \(U_{\mathrm{pack}}\) (GS-B0 \(m_{\mathrm{dyn}}\)); Willmore ladder energy | | Soft glue | Proof of Einstein from bulk geometry alone |
5. Alignment with banked stack
``text Cosmos / Mach m_Mach(G, H0, α, …) [M] O-EMC-2 │ │ P_EMC soft glue a = ħ/(m c) ▼ Face T(1,1) E_path = ħc/a = m c² [E process under package] │ ├─ optional ⟨S⟩ [M] WE face k ├─ dual cancel / hold structure [separate; R-HOLD] └─ Willmore ladder / S⁴ generation [books 2–3 ratios; not this glue] ``
| Prior | Role under \(\mathcal{P}_{\mathrm{EMC}}\) | |-------|------------------------------------------| | M-PHOT | Face energy + Compton ID language — same soft glue, mass source upgraded to Mach when absolute | | GS-B0 | \(E_{\mathrm{path}}\) vs \(m_{\mathrm{dyn}}\) dictionary intact; this card uses path energy, not hold \(U_{\mathrm{pack}}\) | | Weber Meets Einstein | Optional \(k=\langle S\rangle\) only | | M3 / M3-PROJ | Three books; bulk mass ≠ face Willmore imprint | | Absolute scale avenues | Local pure-geometry \(a\) still CLOSED-NULL — why package is soft |
6. How agents should write
| Context | Write | Do not write | |---------|-------|--------------| | Absolute electron mass in programme | \(m_e^{\mathrm{(Mach)}}\) under \(\mathcal{P}_{\mathrm{EMC}}\) | “derived \(m_e\) from first principles” | | Rest energy match | “\(E_{\mathrm{path}}=m c^2\) under soft glue \(a=\hbar/(mc)\)” | “bulk–face theorem proves \(E=mc^2\)” | | WE correction | “optional face \(k=\langle S\rangle\)” | “Weber scalar is bulk mass” | | vs lab | “check vs CODATA; \(H_0\) band ~1–2%” | “\(H_0=69\) proves non-circular absolute” | | Generations | Route E / S7 books | Mach formula for \(m_\mu,m_\tau\) without new package |
7. Kill / pass (package hygiene)
| ID | Claim | Verdict | |----|-------|---------| | EMC3-P0 | Card named; soft vs hard split clear | PASS | | EMC3-P1 | Default glue forces \(E=mc^2\) algebraically | PASS (construction) | | EMC3-P2 | Mach J2 absolute \(m\) free of Compton | PASS as [M] (O-EMC-2) | | EMC3-P3 | Join is a theorem from independent \(a,m\) | FAIL (by design of soft card) | | EMC3-F1 | \(\mathcal{P}_{\mathrm{EMC}}\) ⇒ Einstein derived | FORBIDDEN | | EMC3-F2 | \(\alpha\) derived from Mach invert | FORBIDDEN | | EMC3-F3 | Dual / hold / WE invert replaces \(m_{\mathrm{Mach}}\) | FORBIDDEN under this card | | EMC3-F4 | Silent upgrade soft → theorem | FORBIDDEN | | EMC3-F5 | Local absolute \(a\) reopened without new \(L_\) | FORBIDDEN |
8. Open residuals (outside the card)
| ID | Residual | Status | |----|----------|--------| | O-EMC-hard | Independent \(a\) or \(L_\), then true join test | OPEN (re-open rule: new principle only) | | α-in-Mach | Why \(\alpha\) multiplies \(G\) formula | [M/O] | | √6 anchor | \(R=\sqrt{6}\,c/H_0\) | [M/O] | | \(H_0\) tension | Which cosmological \(H_0\) | [O] | | O-MAN | Shared \(3/(2\alpha)\) across books | OPEN (separate) |
9. Paper sentence
We adopt a named soft package in which the electron’s absolute mass is taken from the Mach cosmological formula and the seat radius is fixed by equating face confinement energy \(\hbar c/a\) to \(m c^2\) (optionally times a face Weber factor \(\langle S\rangle\)); this organises bulk–face bookkeeping without claiming a theorem that independently determined bulk mass and geometric radius must match.
10. One-line for agents
\(\mathcal{P}_{\mathrm{EMC}}\) v1: m=m_Mach [M]; E=ħc/a; soft a=ħ/(mc) ⇒ E=mc² by ID; optional k=⟨S⟩; NOT theorem; not α; not hold.