Pith Number

pith:PJ5CKCE3

pith:2015:PJ5CKCE3XU5VES4P3PKKMBQ3MJ

not attested not anchored not stored refs pending

The spectral gap for transfer operators of torus extensions over expanding maps

Huyi Hu, Jianyu Chen

arxiv:1503.02232 v3 · 2015-03-08 · 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{PJ5CKCE3XU5VES4P3PKKMBQ3MJ}

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	2026-05-17T23:55:05.520736Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a7a25089bbd3b524b8fdbd4a6061b627c35cbd849c4c2916bde787753b1828e

Aliases

arxiv: 1503.02232 · arxiv_version: 1503.02232v3 · doi: 10.48550/arxiv.1503.02232 · pith_short_12: PJ5CKCE3XU5V · pith_short_16: PJ5CKCE3XU5VES4P · pith_short_8: PJ5CKCE3

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/PJ5CKCE3XU5VES4P3PKKMBQ3MJ \
  | 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: 7a7a25089bbd3b524b8fdbd4a6061b627c35cbd849c4c2916bde787753b1828e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb91dbc75bbca8443e6dd1a4fa7c81a5eb035946476b8351fe38a09eb7fd9d70",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-03-08T00:59:15Z",
    "title_canon_sha256": "38f740c2796e112ddcad400b0177132ea75e82a9f793f83adf4759ca93ae2305"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.02232",
    "kind": "arxiv",
    "version": 3
  }
}