Pith Number

pith:ZMK6QY72

pith:2005:ZMK6QY72AZC32MJBMAQWM7BNUR

not attested not anchored not stored refs pending

Local Spectral Density and Vacuum Energy near a Quantum Graph Vertex

Stephen A. Fulling

arxiv:math/0508335 v1 · 2005-08-17 · math.SP · hep-th · 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{ZMK6QY72AZC32MJBMAQWM7BNUR}

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	2026-05-18T01:58:24.476257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb15e863fa0645bd31216021667c2da452b228359fce0717c4fc687d953cde0e

Aliases

arxiv: math/0508335 · arxiv_version: math/0508335v1 · doi: 10.48550/arxiv.math/0508335 · pith_short_12: ZMK6QY72AZC3 · pith_short_16: ZMK6QY72AZC32MJB · pith_short_8: ZMK6QY72

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/ZMK6QY72AZC32MJBMAQWM7BNUR \
  | 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: cb15e863fa0645bd31216021667c2da452b228359fce0717c4fc687d953cde0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f53c522d87e36c70fb5f891b52ff8ff1e65c916fd992c949d3e6608832299e2",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2005-08-17T20:12:49Z",
    "title_canon_sha256": "75d38f997147b586b260adcba9ed0d3e549cf0f2090a011a16f2996a83a98e10"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0508335",
    "kind": "arxiv",
    "version": 1
  }
}