Pith Number

pith:ZTM6BVD4

pith:2015:ZTM6BVD4XO4ZYBYF4WL6AT7W46

not attested not anchored not stored refs pending

Measure preserving actions of affine semigroups and {x+y,xy} patterns

Joel Moreira, Vitaly Bergelson

arxiv:1509.07574 v1 · 2015-09-25 · math.DS · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZTM6BVD4XO4ZYBYF4WL6AT7W46}

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	2026-05-18T01:32:02.446147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ccd9e0d47cbbb99c0705e597e04ff6e7a3e7421b20e295d01835ae9eef79e33e

Aliases

arxiv: 1509.07574 · arxiv_version: 1509.07574v1 · doi: 10.48550/arxiv.1509.07574 · pith_short_12: ZTM6BVD4XO4Z · pith_short_16: ZTM6BVD4XO4ZYBYF · pith_short_8: ZTM6BVD4

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/ZTM6BVD4XO4ZYBYF4WL6AT7W46 \
  | 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: ccd9e0d47cbbb99c0705e597e04ff6e7a3e7421b20e295d01835ae9eef79e33e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7811741b1a921bbcfd60df8be39fadf4904f4dea32f323e1164d85b9e795a6d6",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-09-25T01:33:44Z",
    "title_canon_sha256": "64544cfb4b929da4ad80f1e4cc447dba3c003f1e90f442f49612f064eacd4fd5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07574",
    "kind": "arxiv",
    "version": 1
  }
}