Pith Number

pith:4G7XXFGU

pith:2026:4G7XXFGUAGBYN5E2VUTL4VBENF

not attested not anchored not stored refs pending

Trapped bosons in mean field QED, nonlinear resonance cascades and dynamical BEC formation

Ali Mezher, Thomas Chen

Nonlinear resonance cascades in mean-field QED produce monotone energy decrease in trapped bosons and establish dynamical BEC formation.

arxiv:2604.11756 v3 · 2026-04-13 · math-ph · math.AP · math.MP · quant-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4G7XXFGUAGBYN5E2VUTL4VBENF}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We demonstrate that solutions to this nonlinear cascade describe a monotone decreasing energy flow in the boson subsystem. Thereby, we prove that a Bose-Einstein condensate (BEC) forms dynamically, under conservation of the total boson L2 mass.

C2weakest assumption

The combined weak-coupling and macroscopic time limit applied to the mean-field non-relativistic QED description from Leopold and Pickl (2017) produces the effective nonlinear cascade equations whose solutions exhibit the claimed monotone energy decrease.

C3one line summary

Nonlinear cascade equations derived from mean-field QED for trapped bosons prove dynamical BEC formation via monotone energy flow under conserved L2 mass, distinct from thermal relaxation.

Receipt and verification

First computed	2026-06-03T02:05:47.562766Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1bf7b94d4018386f49aad26be5424697273eb49e73c181bc51b222f5da7f7c9

Aliases

arxiv: 2604.11756 · arxiv_version: 2604.11756v3 · doi: 10.48550/arxiv.2604.11756 · pith_short_12: 4G7XXFGUAGBY · pith_short_16: 4G7XXFGUAGBYN5E2 · pith_short_8: 4G7XXFGU

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4G7XXFGUAGBYN5E2VUTL4VBENF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e1bf7b94d4018386f49aad26be5424697273eb49e73c181bc51b222f5da7f7c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf6aad4593325390144a7a0065c88b3d2f97fa4fdfe2454f96730bfbef48fb7d",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-04-13T17:29:54Z",
    "title_canon_sha256": "99326bf6a6e456b6e00a281b8a297637b807a8da768f36ba645de3ea5f4efe8d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.11756",
    "kind": "arxiv",
    "version": 3
  }
}