Pith Number

pith:3KGVMCKX

pith:2010:3KGVMCKXNINZJEDVROZH5MD4OJ

not attested not anchored not stored refs pending

Asymptotic solution for first and second order integro-differential equations

Mauro Bologna

arxiv:1008.0069 v1 · 2010-07-31 · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3KGVMCKXNINZJEDVROZH5MD4OJ}

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.

Receipt and verification

First computed	2026-05-18T04:42:44.108543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da8d5609576a1b9490758bb27eb07c726b390da57059dde07c9c600e26727bb9

Aliases

arxiv: 1008.0069 · arxiv_version: 1008.0069v1 · doi: 10.48550/arxiv.1008.0069 · pith_short_12: 3KGVMCKXNINZ · pith_short_16: 3KGVMCKXNINZJEDV · pith_short_8: 3KGVMCKX

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/3KGVMCKXNINZJEDVROZH5MD4OJ \
  | 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: da8d5609576a1b9490758bb27eb07c726b390da57059dde07c9c600e26727bb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3920a9635c664108e66cc90c4e166552ec866a41eac92f54e046526e7f7914e2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2010-07-31T08:20:11Z",
    "title_canon_sha256": "e49aef2194a46d8770f8fdca5046bec7fff0116ac368805b4d9f87f3d850c99d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.0069",
    "kind": "arxiv",
    "version": 1
  }
}