Pith Number

pith:SCKT7RZG

pith:2012:SCKT7RZGBO5MC35KR43FDTCGZI

not attested not anchored not stored refs pending

Simply connected Alexandrov 4-manifolds with positive or nonnegative curvature and torus actions

Fernando Galaz-Garcia

arxiv:1208.3041 v2 · 2012-08-15 · 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{SCKT7RZGBO5MC35KR43FDTCGZI}

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	2026-05-18T03:17:14.786983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90953fc7260bbac16faa8f3651cc46ca2d9c28abff3f91fbc466d3ea11f5b7c8

Aliases

arxiv: 1208.3041 · arxiv_version: 1208.3041v2 · doi: 10.48550/arxiv.1208.3041 · pith_short_12: SCKT7RZGBO5M · pith_short_16: SCKT7RZGBO5MC35K · pith_short_8: SCKT7RZG

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/SCKT7RZGBO5MC35KR43FDTCGZI \
  | 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: 90953fc7260bbac16faa8f3651cc46ca2d9c28abff3f91fbc466d3ea11f5b7c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "faf129968c1bbeef0dfb4e5d4a8fbc49090681068b20bd7409f7e1b4a282ce5c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-08-15T06:35:01Z",
    "title_canon_sha256": "44091f99c3bc53b8ce40465d76c5d964a7f7e9fed64613f067e773a40cd0a399"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3041",
    "kind": "arxiv",
    "version": 2
  }
}