Pith Number

pith:XTHS67TS

pith:2010:XTHS67TSSGSTFM4CSOTYOES7JZ

not attested not anchored not stored refs pending

A Hasse diagram for rational toral ranks

Toshihiro Yamaguchi

arxiv:1010.4841 v1 · 2010-10-23 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XTHS67TSSGSTFM4CSOTYOES7JZ}

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	2026-05-18T04:38:50.059893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bccf2f7e7291a532b38293a787125f4e6404dd2caba4d2370439b4baf3563778

Aliases

arxiv: 1010.4841 · arxiv_version: 1010.4841v1 · doi: 10.48550/arxiv.1010.4841 · pith_short_12: XTHS67TSSGST · pith_short_16: XTHS67TSSGSTFM4C · pith_short_8: XTHS67TS

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/XTHS67TSSGSTFM4CSOTYOES7JZ \
  | 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: bccf2f7e7291a532b38293a787125f4e6404dd2caba4d2370439b4baf3563778

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d057bd4da67078fe37566e9f631d615269c60a76986ca674db710a514b63929",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2010-10-23T02:40:00Z",
    "title_canon_sha256": "f1538da6b36ecba1485f42eb06d32167c0916c69544acc55a2ae8ec3f2c62bf0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4841",
    "kind": "arxiv",
    "version": 1
  }
}