Pith Number

pith:PNMRN5DB

pith:2012:PNMRN5DBNJZURULHBX7B6W6ANE

not attested not anchored not stored refs pending

The spectral shift function and Levinson's theorem for quantum star graphs

Semra Demirel

arxiv:1205.1772 v1 · 2012-05-08 · math.SP · 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{PNMRN5DBNJZURULHBX7B6W6ANE}

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	2026-05-18T01:57:36.539488Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b5916f4616a7348d1670dfe1f5bc0693348f8358d24a713d3b564020e48641b

Aliases

arxiv: 1205.1772 · arxiv_version: 1205.1772v1 · doi: 10.48550/arxiv.1205.1772 · pith_short_12: PNMRN5DBNJZU · pith_short_16: PNMRN5DBNJZURULH · pith_short_8: PNMRN5DB

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/PNMRN5DBNJZURULHBX7B6W6ANE \
  | 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: 7b5916f4616a7348d1670dfe1f5bc0693348f8358d24a713d3b564020e48641b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "125579c7c41c14a184897c186d0bd08ee1ab88bca5d8e26bc8c976cc4f8c061a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2012-05-08T18:54:44Z",
    "title_canon_sha256": "2dd5bf53abf11844c37c55e0efdcb4d3624daca72cf8d312ed3fd86c16e1b0e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.1772",
    "kind": "arxiv",
    "version": 1
  }
}