Pith Number

pith:DYMFED5W

pith:2010:DYMFED5WCGADCD3YMTKATAEVPU

not attested not anchored not stored refs pending

Cusped hyperbolic 3-manifolds: canonically CAT(0) with CAT(0) spines

Iain R. Aitchison

arxiv:1008.1468 v1 · 2010-08-09 · 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{DYMFED5WCGADCD3YMTKATAEVPU}

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	2026-05-18T04:42:24.135237Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e18520fb61180310f7864d40980957d11410cd79737c045a07fd40fc024482d

Aliases

arxiv: 1008.1468 · arxiv_version: 1008.1468v1 · doi: 10.48550/arxiv.1008.1468 · pith_short_12: DYMFED5WCGAD · pith_short_16: DYMFED5WCGADCD3Y · pith_short_8: DYMFED5W

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/DYMFED5WCGADCD3YMTKATAEVPU \
  | 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: 1e18520fb61180310f7864d40980957d11410cd79737c045a07fd40fc024482d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e37b90725bc9223a4289a5a3d3a892e16641c5088d1cdadbc74a2e2f3edf1876",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-08-09T08:53:57Z",
    "title_canon_sha256": "ff428aa9ac0b3d807ab6aa197eab2c74f53ba0bc6b2cf001209981f4a1d1d422"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.1468",
    "kind": "arxiv",
    "version": 1
  }
}