Pith Number

pith:CN2VJIZ7

pith:2015:CN2VJIZ7SQIJB2ZGGPLWQSMPAB

not attested not anchored not stored refs pending

A surface with discontinuous isoperimetric profile and expander manifolds

Eric Swenson, Panos Papasoglu

arxiv:1509.02307 v2 · 2015-09-08 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CN2VJIZ7SQIJB2ZGGPLWQSMPAB}

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	2026-05-17T23:40:05.048594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

137554a33f941090eb2633d768498f0056b32980317f839fe9f775df1f16f065

Aliases

arxiv: 1509.02307 · arxiv_version: 1509.02307v2 · doi: 10.48550/arxiv.1509.02307 · pith_short_12: CN2VJIZ7SQIJ · pith_short_16: CN2VJIZ7SQIJB2ZG · pith_short_8: CN2VJIZ7

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/CN2VJIZ7SQIJB2ZGGPLWQSMPAB \
  | 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: 137554a33f941090eb2633d768498f0056b32980317f839fe9f775df1f16f065

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d02e15d9b6dd0ac76a6d1f7545c2f00b2abe2039fb16295c79ca7b5d1db90737",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-09-08T10:10:55Z",
    "title_canon_sha256": "799d8ad00f5aa13386d774e08833a4e45e0eb630c2f9f4393ca07dea99a8aba1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.02307",
    "kind": "arxiv",
    "version": 2
  }
}