Pith Number

pith:ZY5DZ4ZZ

pith:2012:ZY5DZ4ZZZYKX4MSRJSTN3Z6ACJ

not attested not anchored not stored refs pending

Periodic elliptic operators with asymptotically preassigned spectrum

Andrii Khrabustovskyi

arxiv:1201.3729 v2 · 2012-01-18 · math.SP · math-ph · math.AP · 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{ZY5DZ4ZZZYKX4MSRJSTN3Z6ACJ}

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	2026-05-18T04:03:08.725444Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce3a3cf339ce157e32514ca6dde7c0124ff91902f0ffa2753b4d623feb5a1b74

Aliases

arxiv: 1201.3729 · arxiv_version: 1201.3729v2 · doi: 10.48550/arxiv.1201.3729 · pith_short_12: ZY5DZ4ZZZYKX · pith_short_16: ZY5DZ4ZZZYKX4MSR · pith_short_8: ZY5DZ4ZZ

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/ZY5DZ4ZZZYKX4MSRJSTN3Z6ACJ \
  | 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: ce3a3cf339ce157e32514ca6dde7c0124ff91902f0ffa2753b4d623feb5a1b74

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18087797690bd1e07137084568d21e2b21c023aa07cfed882e42d96356661507",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2012-01-18T09:24:49Z",
    "title_canon_sha256": "5e6bd706fb421c6a671185760a4c8c7f7cca7b765bcb141ecf802f798f5c264e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.3729",
    "kind": "arxiv",
    "version": 2
  }
}