Pith Number

pith:4XSYFUAW

pith:2011:4XSYFUAWQENZPJTVLSX7DOVWIS

not attested not anchored not stored refs pending

Some applications of Gabai's internal hierarchy

Yi Ni

arxiv:1111.0914 v2 · 2011-11-03 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4XSYFUAWQENZPJTVLSX7DOVWIS}

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	2026-05-18T03:10:14.661550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5e582d016811b97a6755caff1bab6448f1a286f7a4a19b20c2882a38f69aab3

Aliases

arxiv: 1111.0914 · arxiv_version: 1111.0914v2 · doi: 10.48550/arxiv.1111.0914 · pith_short_12: 4XSYFUAWQENZ · pith_short_16: 4XSYFUAWQENZPJTV · pith_short_8: 4XSYFUAW

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/4XSYFUAWQENZPJTVLSX7DOVWIS \
  | 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: e5e582d016811b97a6755caff1bab6448f1a286f7a4a19b20c2882a38f69aab3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73241c9bc2436577acf03c9dd02443e9d3d7b868b7e71d94b886174e9838bcf5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-11-03T17:01:13Z",
    "title_canon_sha256": "4adde2aa6b0dd6adfbf9c4d956d8b89afdf2c7baffd3727f74b77cfa316e11be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0914",
    "kind": "arxiv",
    "version": 2
  }
}