Pith Number

pith:ND4LFYQK

pith:2012:ND4LFYQKLGTQJ6GZ3B4BMIABFB

not attested not anchored not stored refs pending

Nonexpansive Z^2 subdynamics and Nivat's conjecture

Bryna Kra, Van Cyr

arxiv:1208.4090 v2 · 2012-08-20 · 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{ND4LFYQKLGTQJ6GZ3B4BMIABFB}

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	2026-05-18T03:15:18.696081Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68f8b2e20a59a704f8d9d8781620012872aaa8519f73315b5f0d69c01784f070

Aliases

arxiv: 1208.4090 · arxiv_version: 1208.4090v2 · doi: 10.48550/arxiv.1208.4090 · pith_short_12: ND4LFYQKLGTQ · pith_short_16: ND4LFYQKLGTQJ6GZ · pith_short_8: ND4LFYQK

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/ND4LFYQKLGTQJ6GZ3B4BMIABFB \
  | 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: 68f8b2e20a59a704f8d9d8781620012872aaa8519f73315b5f0d69c01784f070

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ef3aedbb03ec755525f48f6d41b434bc98e46191c5f6fb9e2ae2ce61f47c815",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-08-20T19:45:37Z",
    "title_canon_sha256": "678b6a591ed6f29f15924abe8072f9bcd93ef6212ad1ec68edce5f140841d987"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4090",
    "kind": "arxiv",
    "version": 2
  }
}