Pith Number

pith:MND64QII

pith:2026:MND64QII3M56TMELWRGGTH762N

not attested not anchored not stored refs pending

Critical set for surface diffeomorphisms revisited

Enrique Pujals, Sylvain Crovisier

arxiv:2601.08208 v2 · 2026-01-13 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MND64QII3M56TMELWRGGTH762N}

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	2026-07-29T00:24:34.974098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6347ee4108db3be9b08bb44c699ffed37bf72d07d4d16b7faf11f2ed1ec29127

Aliases

arxiv: 2601.08208 · arxiv_version: 2601.08208v2 · doi: 10.48550/arxiv.2601.08208 · pith_short_12: MND64QII3M56 · pith_short_16: MND64QII3M56TMEL · pith_short_8: MND64QII

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/MND64QII3M56TMELWRGGTH762N \
  | 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: 6347ee4108db3be9b08bb44c699ffed37bf72d07d4d16b7faf11f2ed1ec29127

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2c41fc13368a845aa8c434ed524a090049f3adda99ff1c94a9957b4c4429e4a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-01-13T04:22:30Z",
    "title_canon_sha256": "e9c74d859ff81f01d3a389732dd91053deb9c0c29bc546c6a37fa22ab76b7209"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.08208",
    "kind": "arxiv",
    "version": 2
  }
}