Pith Number

pith:CLLQC5VS

pith:2003:CLLQC5VSX5YQAHR5HYW7I33U47

not attested not anchored not stored refs pending

Discrete Green's functions for products of regular graphs

Robert B. Ellis

arxiv:math/0309080 v2 · 2003-09-04 · math.CO · math.GT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CLLQC5VSX5YQAHR5HYW7I33U47}

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.

Cited by

1 paper in Pith

Giant Heat Flux Effect in Non-Chiral Transmission Lines

Receipt and verification

First computed	2026-07-04T14:37:41.810045Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12d70176b2bf71001e3d3e2df46f74e7e60d87e7becc2e8ec5ee6988361d2b02

Aliases

arxiv: math/0309080 · arxiv_version: math/0309080v2 · doi: 10.48550/arxiv.math/0309080 · pith_short_12: CLLQC5VSX5YQ · pith_short_16: CLLQC5VSX5YQAHR5 · pith_short_8: CLLQC5VS

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/CLLQC5VSX5YQAHR5HYW7I33U47 \
  | 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: 12d70176b2bf71001e3d3e2df46f74e7e60d87e7becc2e8ec5ee6988361d2b02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6c878790c5ec6d7f226e9b8be190163b8be5f30d1e16326fecbb6353834b19c",
    "cross_cats_sorted": [
      "math.GT",
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2003-09-04T19:58:54Z",
    "title_canon_sha256": "b8cd636beb855fff9c82577a05b3067a3b2435f087f7cce7e51d334ef398d215"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0309080",
    "kind": "arxiv",
    "version": 2
  }
}