Pith Number

pith:PKRMXHWD

pith:2026:PKRMXHWDUN5WARISIL24PZL7RY

not attested not anchored not stored refs pending

Lengths of simple closed geodesics on hyperbolic surfaces in prescribed homology classes

Igor M. Patsankov

arxiv:2606.24836 v1 · 2026-06-23 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PKRMXHWDUN5WARISIL24PZL7RY}

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	2026-06-24T01:15:43.572865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7aa2cb9ec3a37b60451242f5c7e57f8e08642688ddf7cb5eab27645031366c88

Aliases

arxiv: 2606.24836 · arxiv_version: 2606.24836v1 · doi: 10.48550/arxiv.2606.24836 · pith_short_12: PKRMXHWDUN5W · pith_short_16: PKRMXHWDUN5WARIS · pith_short_8: PKRMXHWD

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/PKRMXHWDUN5WARISIL24PZL7RY \
  | 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: 7aa2cb9ec3a37b60451242f5c7e57f8e08642688ddf7cb5eab27645031366c88

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8dcfeda26f7b3409aa11dea86257799cd642a0bea8ac5b888c3d9f4bab0cd9b3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-06-23T17:16:09Z",
    "title_canon_sha256": "d498e1025b335f14624f0e775d546d5c1649712990cf5d699371783b43358f21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24836",
    "kind": "arxiv",
    "version": 1
  }
}