Pith Number

pith:RKSMY57D

pith:2013:RKSMY57DHFLK2Q3TC2O3E5HYUB

not attested not anchored not stored refs pending

An elementary proof of Franks' lemma for geodesic flows

Daniel Visscher

arxiv:1307.6573 v2 · 2013-07-24 · 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{RKSMY57DHFLK2Q3TC2O3E5HYUB}

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	2026-05-18T03:05:37.828396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8aa4cc77e33956ad4373169db274f8a06c00c6c5908458d8f2e752936b801402

Aliases

arxiv: 1307.6573 · arxiv_version: 1307.6573v2 · doi: 10.48550/arxiv.1307.6573 · pith_short_12: RKSMY57DHFLK · pith_short_16: RKSMY57DHFLK2Q3T · pith_short_8: RKSMY57D

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/RKSMY57DHFLK2Q3TC2O3E5HYUB \
  | 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: 8aa4cc77e33956ad4373169db274f8a06c00c6c5908458d8f2e752936b801402

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "477897a7767f52226d24d6bded814a035d6ec77d8a8a7ad2cd046d5ee0175ad3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-07-24T20:25:43Z",
    "title_canon_sha256": "58b33c75a990b8489583a478841e60117e6a39cd6f29c1b3605b94fff7f0b54a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.6573",
    "kind": "arxiv",
    "version": 2
  }
}