Pith Number

pith:FW3ZODCQ

pith:2016:FW3ZODCQHSBGFINRK5MBLSCMFA

not attested not anchored not stored refs pending

Second Phase transition line

Artur Avila, Qi Zhou, Svetlana Jitomirskaya

arxiv:1608.01799 v1 · 2016-08-05 · math-ph · math.DS · 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{FW3ZODCQHSBGFINRK5MBLSCMFA}

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	2026-05-18T01:09:44.558973Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2db7970c503c8262a1b1575815c84c28357f2190280ad7deba5a76c093398edc

Aliases

arxiv: 1608.01799 · arxiv_version: 1608.01799v1 · doi: 10.48550/arxiv.1608.01799 · pith_short_12: FW3ZODCQHSBG · pith_short_16: FW3ZODCQHSBGFINR · pith_short_8: FW3ZODCQ

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/FW3ZODCQHSBGFINRK5MBLSCMFA \
  | 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: 2db7970c503c8262a1b1575815c84c28357f2190280ad7deba5a76c093398edc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82716fd690a1b9ed753e490eb0d6b26fd974ec6b434887062525225f6e265cd4",
    "cross_cats_sorted": [
      "math.DS",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-08-05T08:22:08Z",
    "title_canon_sha256": "a417227e242dbd0f21948d8041807fc592e33e1d6c1e8cd891fb6f94a35f86c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.01799",
    "kind": "arxiv",
    "version": 1
  }
}