Pith Number

pith:M3MPHBCR

pith:2013:M3MPHBCRARQH3OWJOPYSIRCZPH

not attested not anchored not stored refs pending

Complex one-frequency cocycles

Artur Avila, Christian Sadel, Svetlana Jitomirskaya

arxiv:1306.1605 v2 · 2013-06-07 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M3MPHBCRARQH3OWJOPYSIRCZPH}

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	2026-05-18T00:48:10.284893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66d8f3845104607dbac973f124445979d92adfb1ba222850c4fb8141d23556e4

Aliases

arxiv: 1306.1605 · arxiv_version: 1306.1605v2 · doi: 10.48550/arxiv.1306.1605 · pith_short_12: M3MPHBCRARQH · pith_short_16: M3MPHBCRARQH3OWJ · pith_short_8: M3MPHBCR

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/M3MPHBCRARQH3OWJOPYSIRCZPH \
  | 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: 66d8f3845104607dbac973f124445979d92adfb1ba222850c4fb8141d23556e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5c991ad7db031cec251d8794e7ed31412fa6c4b8d3134bdeecd97fbe9bfb259",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-06-07T04:27:05Z",
    "title_canon_sha256": "2de7a973f3371027c8f60721fb74f597392482ce59279525db498773aa30eaa2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1605",
    "kind": "arxiv",
    "version": 2
  }
}