Pith Number

pith:KK5OCETN

pith:2016:KK5OCETNORW6PLZRUNKZF5PPLO

not attested not anchored not stored refs pending

A Birman-Series type result for geodesics with infinitely many self-intersections

Jenya Sapir

arxiv:1609.00428 v2 · 2016-09-02 · 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{KK5OCETNORW6PLZRUNKZF5PPLO}

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	2026-05-18T00:50:30.973729Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52bae1126d746de7af31a35592f5ef5b96a19d9c87418f81a5e9d6f3f2471541

Aliases

arxiv: 1609.00428 · arxiv_version: 1609.00428v2 · doi: 10.48550/arxiv.1609.00428 · pith_short_12: KK5OCETNORW6 · pith_short_16: KK5OCETNORW6PLZR · pith_short_8: KK5OCETN

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/KK5OCETNORW6PLZRUNKZF5PPLO \
  | 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: 52bae1126d746de7af31a35592f5ef5b96a19d9c87418f81a5e9d6f3f2471541

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a1dc3ec003272c53fb9a13d12a7cd4d216f192d24cd373fd991c084a19dad80",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-09-02T00:06:04Z",
    "title_canon_sha256": "e722afedd004f871892f681e568ea309230a2127c598e89f130da4ea5d71ed3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.00428",
    "kind": "arxiv",
    "version": 2
  }
}