Pith Number

pith:DHC4WVXM

pith:2015:DHC4WVXMJW5HDQFUXDM7AENEIQ

not attested not anchored not stored refs pending

Asymptotic spectral gap for open partially expanding maps

Fr\'ed\'eric Faure, Tobias Weich

arxiv:1504.06728 v3 · 2015-04-25 · math.DS · math-ph · math.MP · nlin.CD

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DHC4WVXMJW5HDQFUXDM7AENEIQ}

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	2026-05-18T00:38:18.871290Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19c5cb56ec4dba71c0b4b8d9f011a44423711b5bbc4c8d53cbc3a3f8aea78b22

Aliases

arxiv: 1504.06728 · arxiv_version: 1504.06728v3 · doi: 10.48550/arxiv.1504.06728 · pith_short_12: DHC4WVXMJW5H · pith_short_16: DHC4WVXMJW5HDQFU · pith_short_8: DHC4WVXM

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/DHC4WVXMJW5HDQFUXDM7AENEIQ \
  | 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: 19c5cb56ec4dba71c0b4b8d9f011a44423711b5bbc4c8d53cbc3a3f8aea78b22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a00f982470e9af340991cff99f14cf7cc833db26c4783b30420df1fdc0d7796c",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "nlin.CD"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-04-25T14:10:56Z",
    "title_canon_sha256": "16e2e236a48c243e103c53a7aae1aa0701b9e7a306ca0690b25e75a8a0085e43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.06728",
    "kind": "arxiv",
    "version": 3
  }
}