Pith Number

pith:FTOAN4YW

pith:2013:FTOAN4YW2HRAOVJ3VDTVIBL2BT

not attested not anchored not stored refs pending

Minimum ranks of sign patterns via sign vectors and duality

Frank J. Hall, Hein van der Holst, John Sinkovic, Lihua Zhang, Marina Arav, Zhongshan Li

arxiv:1312.6048 v1 · 2013-12-20 · 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{FTOAN4YW2HRAOVJ3VDTVIBL2BT}

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	2026-05-18T03:04:07.250409Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2cdc06f316d1e207553ba8e754057a0ccd61919f9d2529a44baa52bb3c2170cc

Aliases

arxiv: 1312.6048 · arxiv_version: 1312.6048v1 · doi: 10.48550/arxiv.1312.6048 · pith_short_12: FTOAN4YW2HRA · pith_short_16: FTOAN4YW2HRAOVJ3 · pith_short_8: FTOAN4YW

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/FTOAN4YW2HRAOVJ3VDTVIBL2BT \
  | 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: 2cdc06f316d1e207553ba8e754057a0ccd61919f9d2529a44baa52bb3c2170cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53c1e3ae26bffc3a51f64907a895fa0d1b23e952d606c241cb9be324bbd8ff89",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-12-20T17:10:19Z",
    "title_canon_sha256": "705965cf6b0b4659b01d18f65414325fc9ae581fa4eaaa40b412ff24e84131f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.6048",
    "kind": "arxiv",
    "version": 1
  }
}