Pith Number

pith:X66YIPFZ

pith:2009:X66YIPFZV7W6ZBZBLHV24MJF6H

not attested not anchored not stored refs pending

Immersing almost geodesic surfaces in a closed hyperbolic three manifold

Jeremy Kahn, Vladimir Markovic

arxiv:0910.5501 v5 · 2009-10-28 · 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{X66YIPFZV7W6ZBZBLHV24MJF6H}

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	2026-05-18T02:24:46.573904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfbd843cb9afedec872159ebae3125f1f13b1718b86c41847745cf61724cf2e1

Aliases

arxiv: 0910.5501 · arxiv_version: 0910.5501v5 · doi: 10.48550/arxiv.0910.5501 · pith_short_12: X66YIPFZV7W6 · pith_short_16: X66YIPFZV7W6ZBZB · pith_short_8: X66YIPFZ

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/X66YIPFZV7W6ZBZBLHV24MJF6H \
  | 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: bfbd843cb9afedec872159ebae3125f1f13b1718b86c41847745cf61724cf2e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6dcf57a2cb48759f352f033c95b4985c42c9ff137a52656bb165e2936b9a94b7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-10-28T21:44:07Z",
    "title_canon_sha256": "fa8cb25a627c0c91dc2604603038d70a86a8a7545457f01ce71836079b39af02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.5501",
    "kind": "arxiv",
    "version": 5
  }
}