Pith Number

pith:3DUHHBHB

pith:2026:3DUHHBHBEUKGEFIK4MJP46CW4D

not attested not anchored not stored refs pending

Interaction with the Environment via Random Matrices and the Emergence of Classical Field Theory

Alexey A. Kryukov

Classical field configurations arise as coordinates on manifolds of quantum states localized by random-matrix environmental interactions, reproducing equations like the sourced Klein-Gordon from unitary Schrödinger evolution.

arxiv:2604.03778 v2 · 2026-04-04 · quant-ph

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\usepackage{pith}
\pithnumber{3DUHHBHBEUKGEFIK4MJP46CW4D}

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Record completeness

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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

The unitary Schrödinger dynamics, combined with the random-matrix model of system-environment interaction, yields effective diffusion in state space together with repeated localization due to environmental recording. As a result, although field states are not themselves confined near classical configurations, the interaction constrains the particle to probe only a restricted sector of the field, corresponding to a tubular neighborhood of localized field states. The resulting dynamics reproduces classical field equations, including the sourced Klein-Gordon equation and the corresponding force law.

C2weakest assumption

The interaction Hamiltonian effectively exhibits a random-matrix structure that produces the required stochastic yet unitary evolution and localization near the constructed manifolds of states localized near classical field configurations in the joint particle-field state space.

C3one line summary

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-29T01:15:04.764388Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8e87384e1251462150ae312fe7856e0cc27086d4d9af59c9176b5804491caa3

Aliases

arxiv: 2604.03778 · arxiv_version: 2604.03778v2 · doi: 10.48550/arxiv.2604.03778 · pith_short_12: 3DUHHBHBEUKG · pith_short_16: 3DUHHBHBEUKGEFIK · pith_short_8: 3DUHHBHB

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/3DUHHBHBEUKGEFIK4MJP46CW4D \
  | 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: d8e87384e1251462150ae312fe7856e0cc27086d4d9af59c9176b5804491caa3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1cf0e0046fb96a2ff33403964867356b9b2cc1b8d9838bf98fc1709292f77c4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-04-04T16:02:49Z",
    "title_canon_sha256": "41561fa50c4f2b55a3d9d4988cbfd0a909d6ac6f2af45a04f889afa6b588ff29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.03778",
    "kind": "arxiv",
    "version": 2
  }
}