Pith Number

pith:T76JBDOC

pith:2012:T76JBDOCJMJEBRQSKOUXBAUHBV

not attested not anchored not stored refs pending

Upper bounds for dimensions of singularity categories

Hailong Dao, Ryo Takahashi

arxiv:1203.1683 v1 · 2012-03-08 · math.AC · math.AG · math.CT · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T76JBDOCJMJEBRQSKOUXBAUHBV}

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	2026-05-18T04:00:37.276871Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ffc908dc24b1240c61253a97082870d64dceabcc1fbca076cf7a578ead00496

Aliases

arxiv: 1203.1683 · arxiv_version: 1203.1683v1 · doi: 10.48550/arxiv.1203.1683 · pith_short_12: T76JBDOCJMJE · pith_short_16: T76JBDOCJMJEBRQS · pith_short_8: T76JBDOC

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/T76JBDOCJMJEBRQSKOUXBAUHBV \
  | 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: 9ffc908dc24b1240c61253a97082870d64dceabcc1fbca076cf7a578ead00496

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1e84f1437164dc64dcc25b1da7a00f7faa65f01405029ff631ec8f428a5e9e5",
    "cross_cats_sorted": [
      "math.AG",
      "math.CT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2012-03-08T03:00:57Z",
    "title_canon_sha256": "e5ce29e857c3f4cec7f119b5ba5f3ecc40bdaf011270d0d844e3bc6db758c018"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.1683",
    "kind": "arxiv",
    "version": 1
  }
}