Pith Number

pith:CC4KA3GQ

pith:2012:CC4KA3GQ2UFVSCFSNCELF7QWXB

not attested not anchored not stored refs pending

On the Kotani-Last and Schrodinger conjectures

Artur Avila

arxiv:1210.6325 v1 · 2012-10-23 · math.DS · 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{CC4KA3GQ2UFVSCFSNCELF7QWXB}

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	2026-05-18T03:42:32.693884Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10b8a06cd0d50b5908b26888b2fe16b8612f29d75835121dc6329f5b570d61ff

Aliases

arxiv: 1210.6325 · arxiv_version: 1210.6325v1 · doi: 10.48550/arxiv.1210.6325 · pith_short_12: CC4KA3GQ2UFV · pith_short_16: CC4KA3GQ2UFVSCFS · pith_short_8: CC4KA3GQ

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/CC4KA3GQ2UFVSCFSNCELF7QWXB \
  | 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: 10b8a06cd0d50b5908b26888b2fe16b8612f29d75835121dc6329f5b570d61ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "595c49fa0616df7c62aeb8993f29d31d56c0f38fe5bf7004bc8e042ce13a0895",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-10-23T18:42:06Z",
    "title_canon_sha256": "02c2988bd00737509a0654459d09541faedc969bfd591a1270c027df17f83649"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6325",
    "kind": "arxiv",
    "version": 1
  }
}