Pith Number

pith:PCVMCBIZ

pith:2011:PCVMCBIZUMSMXDNK7E64QVZNJP

not attested not anchored not stored refs pending

On the edge-balanced index sets of product graphs

Christopher Raridan, Elliot Krop, Sin-Min Lee

arxiv:1103.4994 v1 · 2011-03-25 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PCVMCBIZUMSMXDNK7E64QVZNJP}

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	2026-05-18T03:00:27.320357Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78aac10519a324cb8daaf93dc8572d4be002ebb4b8d82fda016fda3ac30d6afd

Aliases

arxiv: 1103.4994 · arxiv_version: 1103.4994v1 · doi: 10.48550/arxiv.1103.4994 · pith_short_12: PCVMCBIZUMSM · pith_short_16: PCVMCBIZUMSMXDNK · pith_short_8: PCVMCBIZ

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/PCVMCBIZUMSMXDNK7E64QVZNJP \
  | 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: 78aac10519a324cb8daaf93dc8572d4be002ebb4b8d82fda016fda3ac30d6afd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "557e78006a11412d3f9f2e3f58a6f6ce9fb1cccd5109688cdc67db0fdbaacf38",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-03-25T15:27:54Z",
    "title_canon_sha256": "de90079f6bc6102a2a77b26632e9383a3ab93d3801dc0629d42464a04cb554d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4994",
    "kind": "arxiv",
    "version": 1
  }
}