Pith Number

pith:PKTX65HD

pith:2026:PKTX65HDS7LS4OTB3PBWCVFOV6

not attested not anchored not stored refs pending

Laplace operators on quantum graphs

Arkadiusz Bochniak, Dawid Jasi\'nski, Pawe{\l} Kasprzak

arxiv:2607.18473 v1 · 2026-07-20 · math.OA · math-ph · math.MP · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PKTX65HDS7LS4OTB3PBWCVFOV6}

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	2026-07-22T00:22:50.435291Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7aa77f74e397d72e3a61dbc36154aeaf934a0732598c4c55ee2d9d890acec9a6

Aliases

arxiv: 2607.18473 · arxiv_version: 2607.18473v1 · doi: 10.48550/arxiv.2607.18473 · pith_short_12: PKTX65HDS7LS · pith_short_16: PKTX65HDS7LS4OTB · pith_short_8: PKTX65HD

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/PKTX65HDS7LS4OTB3PBWCVFOV6 \
  | 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: 7aa77f74e397d72e3a61dbc36154aeaf934a0732598c4c55ee2d9d890acec9a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0d689f58ea53e5f4e9c120f6e81e622ddb3403ceacae70582e0ca4594840b9e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.QA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-07-20T19:42:21Z",
    "title_canon_sha256": "39842e56671dda3c464348e20cf94c7b492211a41b6e182d178f9d0b2ea96809"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.18473",
    "kind": "arxiv",
    "version": 1
  }
}