Pith Number

pith:LLTCQG3F

pith:2012:LLTCQG3FJJRABRUTBKEE35UYR3

not attested not anchored not stored refs pending

Spectral Rigidity for Periodic Schr\"odinger Operators in Dimension 2

Alden Waters

arxiv:1203.2901 v3 · 2012-03-13 · math.AP · 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{LLTCQG3FJJRABRUTBKEE35UYR3}

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	2026-05-18T02:46:13.331233Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ae6281b654a6200c6930a884df6988ed11f85aa01b3c0d9f3a431124d5d6631

Aliases

arxiv: 1203.2901 · arxiv_version: 1203.2901v3 · doi: 10.48550/arxiv.1203.2901 · pith_short_12: LLTCQG3FJJRA · pith_short_16: LLTCQG3FJJRABRUT · pith_short_8: LLTCQG3F

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/LLTCQG3FJJRABRUTBKEE35UYR3 \
  | 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: 5ae6281b654a6200c6930a884df6988ed11f85aa01b3c0d9f3a431124d5d6631

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78d32bfe4811a150014a33087dee94cd5921007488d7cea33c595be4e3e001fe",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-03-13T19:23:23Z",
    "title_canon_sha256": "99fb302917cf9fb2723c6d5987d7651089fdd2e81a9ecc07863d012b5b2e6327"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.2901",
    "kind": "arxiv",
    "version": 3
  }
}