Pith Number

pith:23IAFEMJ

pith:2007:23IAFEMJCML6TT5V2UXZSHGNJS

not attested not anchored not stored refs pending

Combinatorial Alexander Duality -- a Short and Elementary Proof

Anders Bj\"orner, Martin Tancer

arxiv:0710.1172 v3 · 2007-10-05 · 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{23IAFEMJCML6TT5V2UXZSHGNJS}

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	2026-05-18T04:10:34.749992Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6d00291891317e9cfb5d52f991ccd4c9c61627ccd9edc67531c92c729ea5bb6

Aliases

arxiv: 0710.1172 · arxiv_version: 0710.1172v3 · doi: 10.48550/arxiv.0710.1172 · pith_short_12: 23IAFEMJCML6 · pith_short_16: 23IAFEMJCML6TT5V · pith_short_8: 23IAFEMJ

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/23IAFEMJCML6TT5V2UXZSHGNJS \
  | 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: d6d00291891317e9cfb5d52f991ccd4c9c61627ccd9edc67531c92c729ea5bb6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "641fb66d0ca0c912558fe3e7a4a209dd679231c91298e155f5a24ba41e3c4583",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2007-10-05T10:28:55Z",
    "title_canon_sha256": "0025412d14b9992a2ead61e4519382a3d6bcedf5b3c42bbbc6cb1b15e3db3e15"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.1172",
    "kind": "arxiv",
    "version": 3
  }
}