Pith Number

pith:IXQZI6XU

pith:2014:IXQZI6XUI4XKVD2CK7AJMGTTX3

not attested not anchored not stored refs pending

A Sharp Lower Bound for the Entropy of Closed Hypersurfaces up to Dimension Six

Jacob Bernstein, Lu Wang

arxiv:1406.2966 v2 · 2014-06-11 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IXQZI6XUI4XKVD2CK7AJMGTTX3}

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	2026-05-18T01:11:51.895492Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

45e1947af4472eaa8f4257c0961a73bef28e33087bc1cee657a332159e6e4a33

Aliases

arxiv: 1406.2966 · arxiv_version: 1406.2966v2 · doi: 10.48550/arxiv.1406.2966 · pith_short_12: IXQZI6XUI4XK · pith_short_16: IXQZI6XUI4XKVD2C · pith_short_8: IXQZI6XU

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/IXQZI6XUI4XKVD2CK7AJMGTTX3 \
  | 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: 45e1947af4472eaa8f4257c0961a73bef28e33087bc1cee657a332159e6e4a33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cce35e18518f40651943bd8507d04845fa52d95d326988c43cb376d2e5041a73",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2014-06-11T17:08:26Z",
    "title_canon_sha256": "4b01d4f7ec91bcfb58dc0d479b5c60fc2b47a52420451f287296b5aa1bef663a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.2966",
    "kind": "arxiv",
    "version": 2
  }
}