Pith Number

pith:GJPGVHFW

pith:2015:GJPGVHFWW3QRIDEN2ZB5IATVGV

not attested not anchored not stored refs pending

Expanding cone and applications to homogeneous dynamics

Ronggang Shi

arxiv:1510.05256 v7 · 2015-10-18 · 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{GJPGVHFWW3QRIDEN2ZB5IATVGV}

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	2026-05-17T23:55:01.467905Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

325e6a9cb6b6e1140c8dd643d40275357088d21799653c6a1f89f8e1612e1d09

Aliases

arxiv: 1510.05256 · arxiv_version: 1510.05256v7 · doi: 10.48550/arxiv.1510.05256 · pith_short_12: GJPGVHFWW3QR · pith_short_16: GJPGVHFWW3QRIDEN · pith_short_8: GJPGVHFW

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/GJPGVHFWW3QRIDEN2ZB5IATVGV \
  | 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: 325e6a9cb6b6e1140c8dd643d40275357088d21799653c6a1f89f8e1612e1d09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48e1b4d21a4b6bcd9c35f8baf4d265589d0eb07d495957b42c72c3c2efafc44f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-10-18T15:08:14Z",
    "title_canon_sha256": "bf736385972243f7cafc58aabe7f0720442424e6f546a9e676be753bac03645a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.05256",
    "kind": "arxiv",
    "version": 7
  }
}