Pith Number

pith:LDOWB6RD

pith:2003:LDOWB6RDSCWPW2PY4L4DSG5PY7

not attested not anchored not stored refs pending

Necessary and Sufficient Conditions in the Spectral Theory of Jacobi Matrices and Schr\"odinger Operators

Barry Simon, David Damanik, Rowan Killip

arxiv:math/0309206 v1 · 2003-09-12 · 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{LDOWB6RDSCWPW2PY4L4DSG5PY7}

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	2026-05-18T02:30:23.143452Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

58dd60fa2390acfb69f8e2f8391bafc7f40f5ca7d9f8e99488a0670e9af9cc8f

Aliases

arxiv: math/0309206 · arxiv_version: math/0309206v1 · doi: 10.48550/arxiv.math/0309206 · pith_short_12: LDOWB6RDSCWP · pith_short_16: LDOWB6RDSCWPW2PY · pith_short_8: LDOWB6RD

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/LDOWB6RDSCWPW2PY4L4DSG5PY7 \
  | 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: 58dd60fa2390acfb69f8e2f8391bafc7f40f5ca7d9f8e99488a0670e9af9cc8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c51c157e0c61b03312ee8d084e5838bcd05008aff2117fb756d02c01c426b241",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2003-09-12T06:11:37Z",
    "title_canon_sha256": "3399b5481c8cf7d682e4203c51ce76c562e4ba940cfe44cbb1d4c97b9a150437"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0309206",
    "kind": "arxiv",
    "version": 1
  }
}