Pith Number

pith:4II56TG7

pith:2015:4II56TG76P2S47QDYV5QSGSWI2

not attested not anchored not stored refs pending

A consequence of the factorisation theorem for polynomial orbits on nilmanifolds

Lilian Matthiesen

arxiv:1509.06030 v1 · 2015-09-20 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4II56TG76P2S47QDYV5QSGSWI2}

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	2026-05-18T01:32:36.053099Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e211df4cdff3f52e7e03c57b091a564697af7815ccdef44280d06f0142e9bb77

Aliases

arxiv: 1509.06030 · arxiv_version: 1509.06030v1 · doi: 10.48550/arxiv.1509.06030 · pith_short_12: 4II56TG76P2S · pith_short_16: 4II56TG76P2S47QD · pith_short_8: 4II56TG7

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/4II56TG76P2S47QDYV5QSGSWI2 \
  | 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: e211df4cdff3f52e7e03c57b091a564697af7815ccdef44280d06f0142e9bb77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4199dc389b5f5bf60bc7602ccb3acca1b350c01ee9f667326a6b8f0e07b0263c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-09-20T17:40:29Z",
    "title_canon_sha256": "bdb39bbb12b3be76dd2f241df8fea025b8661be9bb8d0325cf1fe4e06d73cf3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06030",
    "kind": "arxiv",
    "version": 1
  }
}