Pith Number

pith:MWECYXDG

pith:2008:MWECYXDGAL6EW3PGFIP654B6VH

not attested not anchored not stored refs pending

CAT(0) and CAT(-1) fillings of hyperbolic manifolds

Jason Fox Manning, Koji Fujiwara

arxiv:0901.0056 v1 · 2008-12-31 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MWECYXDGAL6EW3PGFIP654B6VH}

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	2026-05-18T04:34:09.060159Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65882c5c6602fc4b6de62a1feef03ea9ce354b1d2af55ca48c4cfce030ea4b49

Aliases

arxiv: 0901.0056 · arxiv_version: 0901.0056v1 · doi: 10.48550/arxiv.0901.0056 · pith_short_12: MWECYXDGAL6E · pith_short_16: MWECYXDGAL6EW3PG · pith_short_8: MWECYXDG

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/MWECYXDGAL6EW3PGFIP654B6VH \
  | 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: 65882c5c6602fc4b6de62a1feef03ea9ce354b1d2af55ca48c4cfce030ea4b49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c9633551c0438e01de93a869f4412757a12ed257f3c0c8304ae04ee27ac28b1",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2008-12-31T04:36:49Z",
    "title_canon_sha256": "a9b23499392bbec7f77b8192352ee93bb422989039eb44c3a97ba964602d6e94"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.0056",
    "kind": "arxiv",
    "version": 1
  }
}