Pith Number

pith:FKBGNLAZ

pith:2015:FKBGNLAZRQDXIE4A5G52JGOQEL

not attested not anchored not stored refs pending

Volume polynomials and duality algebras of multi-fans

Anton Ayzenberg, Mikiya Masuda

arxiv:1509.03008 v1 · 2015-09-10 · math.CO · math.AC · math.AT · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FKBGNLAZRQDXIE4A5G52JGOQEL}

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

Chern Characteristics and Todd-Hirzebruch Identities for Transpolar Pairs of Toric Spaces

Receipt and verification

First computed	2026-05-18T00:55:28.718741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a8266ac198c07741380e9bba499d022fff73a1d7f38d4af2523fafa45834c06

Aliases

arxiv: 1509.03008 · arxiv_version: 1509.03008v1 · doi: 10.48550/arxiv.1509.03008 · pith_short_12: FKBGNLAZRQDX · pith_short_16: FKBGNLAZRQDXIE4A · pith_short_8: FKBGNLAZ

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/FKBGNLAZRQDXIE4A5G52JGOQEL \
  | 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: 2a8266ac198c07741380e9bba499d022fff73a1d7f38d4af2523fafa45834c06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11a292d03fbfc497068b2f457b6dddd1993ba62699e8ce6a5753e1395df96fab",
    "cross_cats_sorted": [
      "math.AC",
      "math.AT",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-10T04:28:40Z",
    "title_canon_sha256": "ef007abc984136010fec65fc08369bf5ef5c2693f583add8295ad0f32cd973d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.03008",
    "kind": "arxiv",
    "version": 1
  }
}