Pith Number

pith:6WKWB7EP

pith:2005:6WKWB7EPQIJE576BAOBQ6JSPX7

not attested not anchored not stored refs pending

Spectral gap estimates for interacting particle systems via a Bochner-type identity

Anne-Severine Boudou, Gustavo Posta, Paolo Dai Pra, Pietro Caputo

arxiv:math/0505533 v3 · 2005-05-25 · math.PR · 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{6WKWB7EPQIJE576BAOBQ6JSPX7}

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	2026-05-18T04:39:39.644074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f59560fc8f82124effc103830f264fbfc4860a19996e448d59bd2b54ebfc1a53

Aliases

arxiv: math/0505533 · arxiv_version: math/0505533v3 · doi: 10.48550/arxiv.math/0505533 · pith_short_12: 6WKWB7EPQIJE · pith_short_16: 6WKWB7EPQIJE576B · pith_short_8: 6WKWB7EP

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/6WKWB7EPQIJE576BAOBQ6JSPX7 \
  | 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: f59560fc8f82124effc103830f264fbfc4860a19996e448d59bd2b54ebfc1a53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0a7ed7521912c879e37a71956de76c924b28ca409095e4a0e40861b48af4c2d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2005-05-25T09:02:09Z",
    "title_canon_sha256": "8efe086acc769b498141f07be76ed87efbcc47a2c223b32b7f3c62f8be58abb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0505533",
    "kind": "arxiv",
    "version": 3
  }
}