Pith Number

pith:K7CG4IM5

pith:2006:K7CG4IM527536F3FXUGDLU26AL

not attested not anchored not stored refs pending

The Case of Critical Coupling in a Class of Unbounded Jacobi Matrices Exhibiting a First-Order Phase Transition

David Damanik (Caltech), Serguei Naboko (St. Petersburg University)

arxiv:math/0605593 v1 · 2006-05-22 · math.SP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K7CG4IM527536F3FXUGDLU26AL}

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	2026-05-18T02:30:23.108785Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57c46e219dd7fbbf1765bd0c35d35e02e28b78ad828fbe92a83d9c917217a442

Aliases

arxiv: math/0605593 · arxiv_version: math/0605593v1 · doi: 10.48550/arxiv.math/0605593 · pith_short_12: K7CG4IM52753 · pith_short_16: K7CG4IM527536F3F · pith_short_8: K7CG4IM5

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/K7CG4IM527536F3FXUGDLU26AL \
  | 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: 57c46e219dd7fbbf1765bd0c35d35e02e28b78ad828fbe92a83d9c917217a442

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e04404e45f14c595101cbde452893ac472f159296794a7b6407fecc31b9cba1",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2006-05-22T19:00:32Z",
    "title_canon_sha256": "74debbb2effa85938d5698fef85bb6fd227af7f0ce86c32a203644cb82ff1202"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0605593",
    "kind": "arxiv",
    "version": 1
  }
}