Pith Number

pith:5IXKMS63

pith:2013:5IXKMS63OYVMR3OGKZBPVKY4P2

not attested not anchored not stored refs pending

The mass of the product of spheres

Jeff A. Viaclovsky

arxiv:1312.5287 v1 · 2013-12-18 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5IXKMS63OYVMR3OGKZBPVKY4P2}

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	2026-05-18T01:45:44.466058Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea2ea64bdb762ac8edc65642faab1c7e82f5953755a66636f7857a3d2b2443e3

Aliases

arxiv: 1312.5287 · arxiv_version: 1312.5287v1 · doi: 10.48550/arxiv.1312.5287 · pith_short_12: 5IXKMS63OYVM · pith_short_16: 5IXKMS63OYVMR3OG · pith_short_8: 5IXKMS63

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/5IXKMS63OYVMR3OGKZBPVKY4P2 \
  | 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: ea2ea64bdb762ac8edc65642faab1c7e82f5953755a66636f7857a3d2b2443e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "785c260aab22d2d07d92adbd09a54d053a22007814244b519b63541013aa98c7",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-12-18T19:53:01Z",
    "title_canon_sha256": "7dc56886a18856e9a0192ddc0338bc23978e14eeb3c6b96319cd3712bb835701"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.5287",
    "kind": "arxiv",
    "version": 1
  }
}