Pith Number

pith:VGGCPQDQ

pith:2015:VGGCPQDQUWOUS3RMSB47ULUNT5

not attested not anchored not stored refs pending

Pointwise multiple averages for systems with two commuting transformations

Sebastian Donoso, Wenbo Sun

arxiv:1509.09310 v2 · 2015-09-30 · 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{VGGCPQDQUWOUS3RMSB47ULUNT5}

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	2026-05-18T00:51:07.513593Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a98c27c070a59d496e2c9079fa2e8d9f4f6510cd41afe39d0f2fa2929ce3e26d

Aliases

arxiv: 1509.09310 · arxiv_version: 1509.09310v2 · doi: 10.48550/arxiv.1509.09310 · pith_short_12: VGGCPQDQUWOU · pith_short_16: VGGCPQDQUWOUS3RM · pith_short_8: VGGCPQDQ

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/VGGCPQDQUWOUS3RMSB47ULUNT5 \
  | 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: a98c27c070a59d496e2c9079fa2e8d9f4f6510cd41afe39d0f2fa2929ce3e26d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "332640f0bb28ceb33b4eff96263b2cdb59ded57eec4f5cb3261037400b71ac36",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-09-30T19:42:52Z",
    "title_canon_sha256": "667e470a3060e7d74ddb168d5a6e3d58e21d1d4e2c66d9db73c86502ae3c2a1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.09310",
    "kind": "arxiv",
    "version": 2
  }
}