Pith Number

pith:DZE2BZJK

pith:2025:DZE2BZJKJIK432TYDDD2LMTQGE

not attested not anchored not stored refs pending

A New Proof of the Sharp Gordon's Lemma: No Eigenvalues for Schr\"odinger Operators with Almost Repetition Potentials

Wencai Liu

arxiv:2501.03157 v1 · 2025-01-06 · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DZE2BZJKJIK432TYDDD2LMTQGE}

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	2026-07-05T09:57:32.380192Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e49a0e52a4a15cdea7818c7a5b27031202d71763e06bda44beb371f0ce9202b

Aliases

arxiv: 2501.03157 · arxiv_version: 2501.03157v1 · doi: 10.48550/arxiv.2501.03157 · pith_short_12: DZE2BZJKJIK4 · pith_short_16: DZE2BZJKJIK432TY · pith_short_8: DZE2BZJK

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/DZE2BZJKJIK432TYDDD2LMTQGE \
  | 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: 1e49a0e52a4a15cdea7818c7a5b27031202d71763e06bda44beb371f0ce9202b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8d1034968d69b659809d9f893efcecbdbd2f43b3e76fadb587aca2a30603c67",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2025-01-06T17:26:05Z",
    "title_canon_sha256": "52e19ee6eda5cc97179531773b2fb697544980a3a963048ca7d6d0b702b6bea0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.03157",
    "kind": "arxiv",
    "version": 1
  }
}