Pith Number

pith:ZR2VXVP4

pith:2015:ZR2VXVP45GYUNCM6VAE4RXAXJU

not attested not anchored not stored refs pending

Isometry-invariant geodesics and the fundamental group, II

Leonardo Macarini, Marco Mazzucchelli

arxiv:1504.05685 v2 · 2015-04-22 · math.DG · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZR2VXVP45GYUNCM6VAE4RXAXJU}

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	2026-05-18T00:52:04.314904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc755bd5fce9b146899ea809c8dc174d3d01f46af07a961c5dd3baafce42d82d

Aliases

arxiv: 1504.05685 · arxiv_version: 1504.05685v2 · doi: 10.48550/arxiv.1504.05685 · pith_short_12: ZR2VXVP45GYU · pith_short_16: ZR2VXVP45GYUNCM6 · pith_short_8: ZR2VXVP4

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/ZR2VXVP45GYUNCM6VAE4RXAXJU \
  | 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: cc755bd5fce9b146899ea809c8dc174d3d01f46af07a961c5dd3baafce42d82d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c69c0c2ee9848882ec6e2e3ae02222c2ce42edab6911233c63f365e6b9db8db9",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-04-22T07:56:30Z",
    "title_canon_sha256": "d2ff82bd1497119c7e5efd0174cfb9ccbd8d2c1bb3d0ed7efa458ae391373329"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.05685",
    "kind": "arxiv",
    "version": 2
  }
}