Pith Number

pith:QFV7RU6T

pith:2012:QFV7RU6T6U6H47GUMU5EBSZYBB

not attested not anchored not stored refs pending

Exponential coordinates and regularity of groupoid heat kernels

Bing Kwan So

arxiv:1210.4729 v1 · 2012-10-17 · 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{QFV7RU6T6U6H47GUMU5EBSZYBB}

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	2026-05-18T03:42:56.313082Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

816bf8d3d3f53c7e7cd4653a40cb3808597351d53e54a2bc904793ece1c59a61

Aliases

arxiv: 1210.4729 · arxiv_version: 1210.4729v1 · doi: 10.48550/arxiv.1210.4729 · pith_short_12: QFV7RU6T6U6H · pith_short_16: QFV7RU6T6U6H47GU · pith_short_8: QFV7RU6T

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/QFV7RU6T6U6H47GUMU5EBSZYBB \
  | 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: 816bf8d3d3f53c7e7cd4653a40cb3808597351d53e54a2bc904793ece1c59a61

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5164d709325d3b49f31c065bebb51c1d43d07ad03c2ccd40822d279c986b3a1a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-10-17T13:15:08Z",
    "title_canon_sha256": "c343c5706ffac678f40a000081996dca044eea3cead6111b051e9ebe1a792e1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.4729",
    "kind": "arxiv",
    "version": 1
  }
}