Pith Number

pith:KVFWL6DN

pith:2007:KVFWL6DNAZR4BWEDPF4M4WZGO6

not attested not anchored not stored refs pending

A Zoll counterexample to a geodesic length conjecture

Christopher Croke, Florent Balacheff, Mikhail G. Katz

arxiv:0711.1229 v2 · 2007-11-08 · math.DG · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KVFWL6DNAZR4BWEDPF4M4WZGO6}

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	2026-05-18T02:41:17.467038Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

554b65f86d0663c0d8837978ce5b2677971ca5b5958c05046520d46addd1b8ba

Aliases

arxiv: 0711.1229 · arxiv_version: 0711.1229v2 · doi: 10.48550/arxiv.0711.1229 · pith_short_12: KVFWL6DNAZR4 · pith_short_16: KVFWL6DNAZR4BWED · pith_short_8: KVFWL6DN

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/KVFWL6DNAZR4BWEDPF4M4WZGO6 \
  | 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: 554b65f86d0663c0d8837978ce5b2677971ca5b5958c05046520d46addd1b8ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fc10fa380fba935c9539198b27b22c2a460e3d73a6cbf2e6410996a36322eb2",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2007-11-08T09:38:32Z",
    "title_canon_sha256": "b4f8d4321ee122c36ddacb008ce455ee53d1cf70edaa236e5476daa27396f676"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.1229",
    "kind": "arxiv",
    "version": 2
  }
}