Pith Number

pith:ZCII75MW

pith:1998:ZCII75MWDB4O3AZ4GMHBXPCLXP

not attested not anchored not stored refs pending

The boundary of the deformation space of the fundamental group of some hyperbolic 3-manifolds fibering over the circle

Leonid Potyagailo

arxiv:math/9811181 v1 · 1998-11-17 · 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{ZCII75MWDB4O3AZ4GMHBXPCLXP}

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	2026-05-18T01:05:33.511614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8908ff5961878ed833c330e1bbc4bbbe32261f3ff142b273ffb400b74ff5af7

Aliases

arxiv: math/9811181 · arxiv_version: math/9811181v1 · doi: 10.48550/arxiv.math/9811181 · pith_short_12: ZCII75MWDB4O · pith_short_16: ZCII75MWDB4O3AZ4 · pith_short_8: ZCII75MW

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/ZCII75MWDB4O3AZ4GMHBXPCLXP \
  | 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: c8908ff5961878ed833c330e1bbc4bbbe32261f3ff142b273ffb400b74ff5af7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2457dd7cae4b96e62ec08b495dd89ec616a02fc1646dcce2586f081efa697f93",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1998-11-17T00:00:00Z",
    "title_canon_sha256": "51c2ba7fd362903e8b463c183c6575ca176fd47407895f84b54c4e7a797ba752"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9811181",
    "kind": "arxiv",
    "version": 1
  }
}