Pith Number

pith:YP55NUIM

pith:2015:YP55NUIMP3SEFECWI7RQSWQMSQ

not attested not anchored not stored refs pending

Franks' Lemma for C^2-Man\'e Perturbations of Riemannian Metrics and Applications to Persistence

Ayadi Lazrag, Ludovic Rifford, Rafael Ruggiero

arxiv:1502.01145 v1 · 2015-02-04 · math.DS · math.DG · 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{YP55NUIMP3SEFECWI7RQSWQMSQ}

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	2026-05-18T02:27:57.892533Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3fbd6d10c7ee442905647e3095a0c940f03083b966d127c602ca804e19a3620

Aliases

arxiv: 1502.01145 · arxiv_version: 1502.01145v1 · doi: 10.48550/arxiv.1502.01145 · pith_short_12: YP55NUIMP3SE · pith_short_16: YP55NUIMP3SEFECW · pith_short_8: YP55NUIM

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/YP55NUIMP3SEFECWI7RQSWQMSQ \
  | 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: c3fbd6d10c7ee442905647e3095a0c940f03083b966d127c602ca804e19a3620

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21e27108eab300b11b70a46fbab3c3274ee7aa16ca438f7f26ed3b95c1380398",
    "cross_cats_sorted": [
      "math.DG",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-02-04T10:16:39Z",
    "title_canon_sha256": "8fb41301f9f1f30f52b486821441cc008ad79158bba185d22cf3198acd76b6d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.01145",
    "kind": "arxiv",
    "version": 1
  }
}