Pith Number

pith:SPF2NH76

pith:2012:SPF2NH76XBXASSDDBTHI757UVH

not attested not anchored not stored refs pending

Collapsing three-dimensional closed Alexandrov spaces with a lower curvature bound

Ayato Mitsuishi, Takao Yamaguchi

arxiv:1212.2302 v1 · 2012-12-11 · math.MG · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SPF2NH76XBXASSDDBTHI757UVH}

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	2026-05-18T03:38:45.364614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93cba69ffeb86e0948630cce8ff7f4a9c000c8c91800d589d10817c8f4961123

Aliases

arxiv: 1212.2302 · arxiv_version: 1212.2302v1 · doi: 10.48550/arxiv.1212.2302 · pith_short_12: SPF2NH76XBXA · pith_short_16: SPF2NH76XBXASSDD · pith_short_8: SPF2NH76

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/SPF2NH76XBXASSDDBTHI757UVH \
  | 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: 93cba69ffeb86e0948630cce8ff7f4a9c000c8c91800d589d10817c8f4961123

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5551e0226690d607c75ef8fba8296147ac6a6d9db2adb2ae8f4b65d0773dafd9",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-12-11T05:07:36Z",
    "title_canon_sha256": "5be1a4a1b685f1f291b762c7d94cb97e48973c3d73ffea217358ec0b36059220"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2302",
    "kind": "arxiv",
    "version": 1
  }
}