Pith Number

pith:E4UBSRFM

pith:2005:E4UBSRFMOHMOEDUVB73WZSY4FU

not attested not anchored not stored refs pending

The Borg-Marchenko Theorem with a Continuous Spectrum

Ricardo Weder, Tuncay Aktosun

arxiv:math-ph/0512001 v1 · 2005-12-01 · 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{E4UBSRFMOHMOEDUVB73WZSY4FU}

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	2026-07-04T14:52:11.490645Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

27281944ac71d8e20e950ff76ccb1c2d162a1196d0390322a571c9c956a8b8e7

Aliases

arxiv: math-ph/0512001 · arxiv_version: math-ph/0512001v1 · doi: 10.48550/arxiv.math-ph/0512001 · pith_short_12: E4UBSRFMOHMO · pith_short_16: E4UBSRFMOHMOEDUV · pith_short_8: E4UBSRFM

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/E4UBSRFMOHMOEDUVB73WZSY4FU \
  | 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: 27281944ac71d8e20e950ff76ccb1c2d162a1196d0390322a571c9c956a8b8e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "609de3d0bb7d13c49bfd60e99c974b5549ff6fb994700227caa9402fb9062b20",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2005-12-01T00:34:36Z",
    "title_canon_sha256": "662e3136f1d5b3ac6071e0e02c255065675415425b756738c7abb167abd605f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0512001",
    "kind": "arxiv",
    "version": 1
  }
}