Pith Number

pith:MFPOZY72

pith:2004:MFPOZY72VCYZ7PGKWTDX2VA6U7

not attested not anchored not stored refs pending

Mean-Field Limit of Quantum Bose Gases and Nonlinear Hartree Equation

Enno Lenzmann, Juerg Froehlich

arxiv:math-ph/0409019 v1 · 2004-09-09 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MFPOZY72VCYZ7PGKWTDX2VA6U7}

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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.

Cited by

1 paper in Pith

The fractional in time Schr\"{o}dinger equation with a Hartree perturbation

Receipt and verification

First computed	2026-07-04T14:34:01.995816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

615eece3faa8b19fbccab4c77d541ea7e3c2759d48ec0bad0b741809dcdc3c38

Aliases

arxiv: math-ph/0409019 · arxiv_version: math-ph/0409019v1 · doi: 10.48550/arxiv.math-ph/0409019 · pith_short_12: MFPOZY72VCYZ · pith_short_16: MFPOZY72VCYZ7PGK · pith_short_8: MFPOZY72

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/MFPOZY72VCYZ7PGKWTDX2VA6U7 \
  | 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: 615eece3faa8b19fbccab4c77d541ea7e3c2759d48ec0bad0b741809dcdc3c38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65b46e618f5be7ef2258b7f8a5be9d35357e411f89ed5aff2cdbee903609699c",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2004-09-09T13:33:01Z",
    "title_canon_sha256": "71959a5c6cc8ea5639ac00e892420227b4a2f31a3e45a3b8eb448f8976601188"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0409019",
    "kind": "arxiv",
    "version": 1
  }
}