Pith Number

pith:A5MZ2BMD

pith:2013:A5MZ2BMDK6UJN4IVWMJMMZKL7G

not attested not anchored not stored refs pending

Random Walks on Simplicial Complexes and Harmonics

John Steenbergen, Sayan Mukherjee

arxiv:1310.5099 v1 · 2013-10-18 · math.CO · math.PR · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A5MZ2BMDK6UJN4IVWMJMMZKL7G}

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	2026-05-18T03:10:01.077976Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07599d058357a896f115b312c6654bf9892905e6ca3418e856f2184cd4f43d28

Aliases

arxiv: 1310.5099 · arxiv_version: 1310.5099v1 · doi: 10.48550/arxiv.1310.5099 · pith_short_12: A5MZ2BMDK6UJ · pith_short_16: A5MZ2BMDK6UJN4IV · pith_short_8: A5MZ2BMD

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/A5MZ2BMDK6UJN4IVWMJMMZKL7G \
  | 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: 07599d058357a896f115b312c6654bf9892905e6ca3418e856f2184cd4f43d28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6767ba4013bb2e29da29a838ff23487fe0fe6297f9a25a14d6827d154d0ff87a",
    "cross_cats_sorted": [
      "math.PR",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-10-18T17:23:24Z",
    "title_canon_sha256": "23fb8d8f0e6f367bff1666a1432e0b65148d2f107fd8445c7089282158bf402b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.5099",
    "kind": "arxiv",
    "version": 1
  }
}