Pith Number

pith:KHW4ED4T

pith:2007:KHW4ED4TZVVNM5C5VO4PIYS5DG

not attested not anchored not stored refs pending

Signed-eliminable graphs and free multiplicities on the braid arrangement

Koji Nuida, Takuro Abe, Yasuhide Numata

arxiv:0712.4110 v3 · 2007-12-26 · math.AC · math.AG · 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{KHW4ED4TZVVNM5C5VO4PIYS5DG}

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	2026-05-18T00:39:16.421418Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51edc20f93cd6ad6745dabb8f4625d1995595b85966908c24883ea3ca217ae8c

Aliases

arxiv: 0712.4110 · arxiv_version: 0712.4110v3 · doi: 10.48550/arxiv.0712.4110 · pith_short_12: KHW4ED4TZVVN · pith_short_16: KHW4ED4TZVVNM5C5 · pith_short_8: KHW4ED4T

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/KHW4ED4TZVVNM5C5VO4PIYS5DG \
  | 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: 51edc20f93cd6ad6745dabb8f4625d1995595b85966908c24883ea3ca217ae8c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "066b0ba9c78337c07325d34089e8ea1a3a11b15dd0cca5a15f7d65098275df65",
    "cross_cats_sorted": [
      "math.AG",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2007-12-26T16:31:08Z",
    "title_canon_sha256": "635999213e0037883ba3ef3c7fecb79297178a59852492f800e3271844c82a68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.4110",
    "kind": "arxiv",
    "version": 3
  }
}