Pith Number

pith:KE7T4XJJ

pith:2015:KE7T4XJJA55PUEVK5BTHG4TWWB

not attested not anchored not stored refs pending

Topological Entropy of Left-Invariant Magnetic Flows on 2-Step Nilmanifolds

Jonathan Epstein

arxiv:1512.02612 v1 · 2015-12-08 · math.DS · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KE7T4XJJA55PUEVK5BTHG4TWWB}

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	2026-05-18T01:24:44.282800Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

513f3e5d29077afa12aae866737276b04b3b683149b316a56008970122e0f4f2

Aliases

arxiv: 1512.02612 · arxiv_version: 1512.02612v1 · doi: 10.48550/arxiv.1512.02612 · pith_short_12: KE7T4XJJA55P · pith_short_16: KE7T4XJJA55PUEVK · pith_short_8: KE7T4XJJ

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/KE7T4XJJA55PUEVK5BTHG4TWWB \
  | 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: 513f3e5d29077afa12aae866737276b04b3b683149b316a56008970122e0f4f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f178a40fcdc5ac59adf36f3be6d4867fbcbc93606d3eab8a3bd35da6b02d17b0",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-12-08T20:06:23Z",
    "title_canon_sha256": "bd0a8e7c8840309f4a850e7a79b06d2cee5ebd90542bb815161d4f2d28a54686"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02612",
    "kind": "arxiv",
    "version": 1
  }
}