Pith Number

pith:GHBBLF2X

pith:2011:GHBBLF2XXKY5ADGSPYMZN2IYHA

not attested not anchored not stored refs pending

Dual complementary polynomials of graphs and combinatorial interpretation on the values of the Tutte polynomial at positive integers

Beifang Chen

arxiv:1105.2675 v2 · 2011-05-13 · 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{GHBBLF2XXKY5ADGSPYMZN2IYHA}

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	2026-05-18T03:21:32.050105Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31c2159757bab1d00cd27e1996e9183810ed556d131180afc1bf8c5b66513d4f

Aliases

arxiv: 1105.2675 · arxiv_version: 1105.2675v2 · doi: 10.48550/arxiv.1105.2675 · pith_short_12: GHBBLF2XXKY5 · pith_short_16: GHBBLF2XXKY5ADGS · pith_short_8: GHBBLF2X

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/GHBBLF2XXKY5ADGSPYMZN2IYHA \
  | 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: 31c2159757bab1d00cd27e1996e9183810ed556d131180afc1bf8c5b66513d4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2bb36a812043e6114cd97e3dbf55fd0b0c0bf630a60076f1eaf969f68ce64d3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-05-13T09:58:30Z",
    "title_canon_sha256": "9baeadcda88a5c7a0ff46d55be653024e74655c104f2868f2f1c4256d88e3ab7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2675",
    "kind": "arxiv",
    "version": 2
  }
}