Pith Number

pith:47VQC3IO

pith:2021:47VQC3IODRLINL7C4SKSHSAAGJ

not attested not anchored not stored refs pending

Products of polymatroids with the strong exchange property

Lisa Nicklasson

arxiv:2101.03081 v3 · 2021-01-08 · math.AC · 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{47VQC3IODRLINL7C4SKSHSAAGJ}

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	2026-07-05T03:49:08.293205Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7eb016d0e1c5686afe2e49523c800326c6e4bd568baf26e8ce36e69a01b8946

Aliases

arxiv: 2101.03081 · arxiv_version: 2101.03081v3 · doi: 10.48550/arxiv.2101.03081 · pith_short_12: 47VQC3IODRLI · pith_short_16: 47VQC3IODRLINL7C · pith_short_8: 47VQC3IO

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/47VQC3IODRLINL7C4SKSHSAAGJ \
  | 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: e7eb016d0e1c5686afe2e49523c800326c6e4bd568baf26e8ce36e69a01b8946

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c0add9182742ffe20cfa4a29b4c12624a3044865ac710d01e743e531b580030",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2021-01-08T16:16:31Z",
    "title_canon_sha256": "4176349752d48fe7522a1a42c7f3b8e0cc5955cb43c11784680710c077a48796"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2101.03081",
    "kind": "arxiv",
    "version": 3
  }
}