Pith Number

pith:4V5MRGI7

pith:2013:4V5MRGI7MINKDPKGNDSFH4Y3O6

not attested not anchored not stored refs pending

On the multiplicity of isometry-invariant geodesics on product manifolds

Marco Mazzucchelli

arxiv:1307.7404 v1 · 2013-07-28 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4V5MRGI7MINKDPKGNDSFH4Y3O6}

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	2026-05-18T02:41:42.262518Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e57ac8991f621aa1bd4668e453f31b7793824105c72fcd73a5ec05d843a73c56

Aliases

arxiv: 1307.7404 · arxiv_version: 1307.7404v1 · doi: 10.48550/arxiv.1307.7404 · pith_short_12: 4V5MRGI7MINK · pith_short_16: 4V5MRGI7MINKDPKG · pith_short_8: 4V5MRGI7

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/4V5MRGI7MINKDPKGNDSFH4Y3O6 \
  | 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: e57ac8991f621aa1bd4668e453f31b7793824105c72fcd73a5ec05d843a73c56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72c80c239110740fb8233b1e8ea3edaf03a6bc0e56aab16d9a3dc79e1e95206d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-07-28T21:11:59Z",
    "title_canon_sha256": "34f8b67b6adafcf4411c421e8131f926b6a63ceffe4d4c20398ca0e8e56d8d9f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.7404",
    "kind": "arxiv",
    "version": 1
  }
}