Pith Number

pith:ELW3XCH6

pith:2012:ELW3XCH6YJWBBONRS57GEDPAMB

not attested not anchored not stored refs pending

Dirac operators and geodesic metric on the harmonic Sierpinski gasket and other fractal sets

Jonathan J. Sarhad, Michel L. Lapidus

arxiv:1212.0878 v3 · 2012-12-04 · math.MG · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ELW3XCH6YJWBBONRS57GEDPAMB}

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	2026-05-18T01:49:56.243271Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22edbb88fec26c10b9b1977e620de0604eafe87386c691da4c8c66e8f803dfa4

Aliases

arxiv: 1212.0878 · arxiv_version: 1212.0878v3 · doi: 10.48550/arxiv.1212.0878 · pith_short_12: ELW3XCH6YJWB · pith_short_16: ELW3XCH6YJWBBONR · pith_short_8: ELW3XCH6

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/ELW3XCH6YJWBBONRS57GEDPAMB \
  | 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: 22edbb88fec26c10b9b1977e620de0604eafe87386c691da4c8c66e8f803dfa4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a51d28acc01c55e4b63467cd7ab84d14bbcd6d5169887a2c7efdeea87d2e822c",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-12-04T21:22:49Z",
    "title_canon_sha256": "2e7b00f090eb815a43c5801baae756822c207db0ad95ffcaddd0d19c2f4dacf4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0878",
    "kind": "arxiv",
    "version": 3
  }
}