Pith Number

pith:KR2TLWZX

pith:2012:KR2TLWZXS4PXCIYN3RL7M6KWNK

not attested not anchored not stored refs pending

A subgroup formula for f-invariant entropy

Brandon Seward

arxiv:1202.5071 v3 · 2012-02-23 · 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{KR2TLWZXS4PXCIYN3RL7M6KWNK}

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	2026-05-18T03:52:38.484585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

547535db37971f71230ddc57f679566a88f43ffdaf6845225cd3fa65486bf7a2

Aliases

arxiv: 1202.5071 · arxiv_version: 1202.5071v3 · doi: 10.48550/arxiv.1202.5071 · pith_short_12: KR2TLWZXS4PX · pith_short_16: KR2TLWZXS4PXCIYN · pith_short_8: KR2TLWZX

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/KR2TLWZXS4PXCIYN3RL7M6KWNK \
  | 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: 547535db37971f71230ddc57f679566a88f43ffdaf6845225cd3fa65486bf7a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b02b17e2b21b42a424f717101c515eef55a2228704945f0415dcc61400bfe25",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-02-23T00:58:52Z",
    "title_canon_sha256": "7349d739becbd9ff0027bcae79d3bae99d4f42fdfe64f97d2d6c31c20a84860c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.5071",
    "kind": "arxiv",
    "version": 3
  }
}