Pith Number

pith:4KJHJ556

pith:2012:4KJHJ5566PN75KJITI6ZZFAAGT

not attested not anchored not stored refs pending

Bounds on minors of binary matrices

Judy-anne H. Osborn, Richard P. Brent

arxiv:1208.3330 v3 · 2012-08-16 · 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{4KJHJ5566PN75KJITI6ZZFAAGT}

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	2026-05-18T03:13:56.250387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e29274f7bef3dbfea9289a3d9c940034db7e858645148cc1f385ae3f956ed525

Aliases

arxiv: 1208.3330 · arxiv_version: 1208.3330v3 · doi: 10.48550/arxiv.1208.3330 · pith_short_12: 4KJHJ5566PN7 · pith_short_16: 4KJHJ5566PN75KJI · pith_short_8: 4KJHJ556

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/4KJHJ5566PN75KJITI6ZZFAAGT \
  | 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: e29274f7bef3dbfea9289a3d9c940034db7e858645148cc1f385ae3f956ed525

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d706f5feb88eae2c7de39bb8d221a8144720b08ded62b9ce9cc71f5cc77acd7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-08-16T10:09:04Z",
    "title_canon_sha256": "111c3b2616fd0cacc41aaffd84b42571982d1b63d0448ba510a30ab2228279b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3330",
    "kind": "arxiv",
    "version": 3
  }
}