Pith Number

pith:AXNBYPUL

pith:2009:AXNBYPULZVUMQVBQHQXTDM6Q3T

not attested not anchored not stored refs pending

Equivariant heat invariants of the Laplacian and nonmininmal operators on differential forms

Yong Wang

arxiv:0907.5456 v2 · 2009-07-31 · math.DG · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AXNBYPULZVUMQVBQHQXTDM6Q3T}

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	2026-05-18T02:46:31.771372Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05da1c3e8bcd68c854303c2f31b3d0dce5a8227ebe2cb8e0d576fdea47e53b0d

Aliases

arxiv: 0907.5456 · arxiv_version: 0907.5456v2 · doi: 10.48550/arxiv.0907.5456 · pith_short_12: AXNBYPULZVUM · pith_short_16: AXNBYPULZVUMQVBQ · pith_short_8: AXNBYPUL

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/AXNBYPULZVUMQVBQHQXTDM6Q3T \
  | 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: 05da1c3e8bcd68c854303c2f31b3d0dce5a8227ebe2cb8e0d576fdea47e53b0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11f0e040c2adb3e57974277a267ba0cb2500be3d86c265261f7f3aa5ecb590d0",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-07-31T02:37:19Z",
    "title_canon_sha256": "88634128a22496c52e2fb090a1718efcdde123f218a8deb7156bd73579a5e0ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.5456",
    "kind": "arxiv",
    "version": 2
  }
}