Pith Number

pith:ZKYCLKL3

pith:2015:ZKYCLKL3WFN6U45XYWMXYNGXRG

not attested not anchored not stored refs pending

Entropy, volume growth and SRB measures for Banach space mappings

Alex Blumenthal, Lai-Sang Young

arxiv:1510.04312 v1 · 2015-10-14 · 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{ZKYCLKL3WFN6U45XYWMXYNGXRG}

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	2026-05-18T01:30:07.512065Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cab025a97bb15bea73b7c5997c34d789af640eefe9362d537bc2efce4a39bb4e

Aliases

arxiv: 1510.04312 · arxiv_version: 1510.04312v1 · doi: 10.48550/arxiv.1510.04312 · pith_short_12: ZKYCLKL3WFN6 · pith_short_16: ZKYCLKL3WFN6U45X · pith_short_8: ZKYCLKL3

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/ZKYCLKL3WFN6U45XYWMXYNGXRG \
  | 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: cab025a97bb15bea73b7c5997c34d789af640eefe9362d537bc2efce4a39bb4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fe7f50886489b75ec3612b74f5c574eee5056ce1feb6196acaac4643b6f32b6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-10-14T20:58:34Z",
    "title_canon_sha256": "d4df5b974bfc631ab5a6b059e35b1df500bf643c1f8d8b2addd22088d0cf32e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.04312",
    "kind": "arxiv",
    "version": 1
  }
}