Pith Number

pith:XJ7NA2F5

pith:2017:XJ7NA2F5HKCJRO7FIZYTHCPRY4

not attested not anchored not stored refs pending

Asymptotic expansion of the mean-field approximation

Mario Pulvirenti, Thierry Paul (CMLS)

arxiv:1710.03618 v1 · 2017-10-10 · quant-ph · math-ph · math.AP · math.DS · math.MP

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

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.

Receipt and verification

First computed	2026-05-18T00:33:11.196838Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba7ed068bd3a8498bbe546713389f1c73d05f0244306c7fe1ed777b52db2a753

Aliases

arxiv: 1710.03618 · arxiv_version: 1710.03618v1 · doi: 10.48550/arxiv.1710.03618 · pith_short_12: XJ7NA2F5HKCJ · pith_short_16: XJ7NA2F5HKCJRO7F · pith_short_8: XJ7NA2F5

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/XJ7NA2F5HKCJRO7FIZYTHCPRY4 \
  | 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: ba7ed068bd3a8498bbe546713389f1c73d05f0244306c7fe1ed777b52db2a753

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3670a5f16143bdbb294da16dcdcbc3ff3c6ab7a907dd663b76cb4cb7c8a51a0c",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2017-10-10T14:14:35Z",
    "title_canon_sha256": "a321076275372389acef9515eaf735a70f032dcf87fab93c57bd79a2767762f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.03618",
    "kind": "arxiv",
    "version": 1
  }
}