Pith Number

pith:CMAT75LF

pith:2013:CMAT75LFX4FUVP2Y5L5YWE7FAN

not attested not anchored not stored refs pending

A generalization of the Cai--Galloway splitting theorem to smooth metric measure spaces

Jeffrey S. Case, Peng Wu

arxiv:1307.0848 v1 · 2013-07-02 · 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{CMAT75LFX4FUVP2Y5L5YWE7FAN}

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	2026-05-18T03:19:23.894234Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13013ff565bf0b4abf58eafb8b13e5035cde7a798a8eb70313d7c50a514164de

Aliases

arxiv: 1307.0848 · arxiv_version: 1307.0848v1 · doi: 10.48550/arxiv.1307.0848 · pith_short_12: CMAT75LFX4FU · pith_short_16: CMAT75LFX4FUVP2Y · pith_short_8: CMAT75LF

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/CMAT75LFX4FUVP2Y5L5YWE7FAN \
  | 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: 13013ff565bf0b4abf58eafb8b13e5035cde7a798a8eb70313d7c50a514164de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc7c3c11294ecb6a22704e4d60fe7d642cb2fa476e22d6eca6b38ff01b6687dc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2013-07-02T20:53:05Z",
    "title_canon_sha256": "1e9f7a403145f75d198ad20839a96547ec16b284bdd46c4c0ebffd03d41f9545"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.0848",
    "kind": "arxiv",
    "version": 1
  }
}