Pith Number

pith:ZBUGF3YH

pith:2010:ZBUGF3YHOCOBZHTE7QN3CXYR6Z

not attested not anchored not stored refs pending

The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry

Bernard Bonnard (IMB), Gabriel Janin (IMB), Gr\'egoire Charlot (IF), Roberta Ghezzi (SISSA/ISAS)

arxiv:1009.2612 v1 · 2010-09-14 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZBUGF3YHOCOBZHTE7QN3CXYR6Z}

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	2026-05-18T04:40:56.709413Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c86862ef07709c1c9e64fc1bb15f11f65bced55994d43576821dd92508b29d6d

Aliases

arxiv: 1009.2612 · arxiv_version: 1009.2612v1 · doi: 10.48550/arxiv.1009.2612 · pith_short_12: ZBUGF3YHOCOB · pith_short_16: ZBUGF3YHOCOBZHTE · pith_short_8: ZBUGF3YH

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/ZBUGF3YHOCOBZHTE7QN3CXYR6Z \
  | 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: c86862ef07709c1c9e64fc1bb15f11f65bced55994d43576821dd92508b29d6d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce008d98356ca3bad39f55620334655d9bbfe403b7356301b7300a6e9927690b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2010-09-14T10:07:22Z",
    "title_canon_sha256": "e8e91794e167cbc74372045be142d34b68997af1c262ea30af2bb848dbaaed76"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2612",
    "kind": "arxiv",
    "version": 1
  }
}