Pith Number

pith:XJ2I7V7H

pith:2016:XJ2I7V7HA4SQMDT442DH47HIPQ

not attested not anchored not stored refs pending

Exhaustion of the curve graph via rigid expansions

Jes\'us Hern\'andez Hern\'andez

arxiv:1611.08010 v1 · 2016-11-23 · 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{XJ2I7V7HA4SQMDT442DH47HIPQ}

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	2026-05-18T00:56:44.693022Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba748fd7e70725060e7ce6867e7ce87c1f3e48190c651b86397a8c5391f14485

Aliases

arxiv: 1611.08010 · arxiv_version: 1611.08010v1 · doi: 10.48550/arxiv.1611.08010 · pith_short_12: XJ2I7V7HA4SQ · pith_short_16: XJ2I7V7HA4SQMDT4 · pith_short_8: XJ2I7V7H

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/XJ2I7V7HA4SQMDT442DH47HIPQ \
  | 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: ba748fd7e70725060e7ce6867e7ce87c1f3e48190c651b86397a8c5391f14485

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a9422c98f83af23c125887fcf5f13ccd3e8226f9f986cad4e6b479d19d6a21f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-11-23T21:32:34Z",
    "title_canon_sha256": "0a279d9cfc4fe171aa91725799a6961797650896e83ca6d76cdea412db4e9885"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.08010",
    "kind": "arxiv",
    "version": 1
  }
}