Pith Number

pith:4KS4AWMU

pith:2015:4KS4AWMUF4XVLFWY6NHAI2ECUG

not attested not anchored not stored refs pending

Enumerative Combinatorics of Simplicial and Cell Complexes: Kirchhoff and Trent Type Theorems

Edward Y. Miller, Sylvain E. Cappell

arxiv:1506.03881 v2 · 2015-06-12 · 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{4KS4AWMUF4XVLFWY6NHAI2ECUG}

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	2026-05-18T00:54:09.092968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2a5c059942f2f5596d8f34e046882a19d183b41638f4b19319410c835e68e1a

Aliases

arxiv: 1506.03881 · arxiv_version: 1506.03881v2 · doi: 10.48550/arxiv.1506.03881 · pith_short_12: 4KS4AWMUF4XV · pith_short_16: 4KS4AWMUF4XVLFWY · pith_short_8: 4KS4AWMU

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/4KS4AWMUF4XVLFWY6NHAI2ECUG \
  | 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: e2a5c059942f2f5596d8f34e046882a19d183b41638f4b19319410c835e68e1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e30c6bd73260e3364fdb2fe7684ca8881436e7d1ee466a1d7df646c5985f168",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-06-12T00:57:45Z",
    "title_canon_sha256": "85e3e61a264c179143cd1b5bbcf49228203bfe53aae82c2b811600bb9be9e94b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.03881",
    "kind": "arxiv",
    "version": 2
  }
}