Pith Number

pith:GFAO4QSU

pith:2013:GFAO4QSUEV2536FBMPCQC2P3QP

not attested not anchored not stored refs pending

Finite p-groups, entropy vectors and the Ingleton inequality for nilpotent groups

Pirita Paajanen

arxiv:1308.2069 v1 · 2013-08-09 · cs.IT · math.GR · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GFAO4QSUEV2536FBMPCQC2P3QP}

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	2026-05-18T03:16:18.306987Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3140ee42542575ddf8a163c50169fb83ee6de7a47a8e6e4e8affb958c2b6a0f6

Aliases

arxiv: 1308.2069 · arxiv_version: 1308.2069v1 · doi: 10.48550/arxiv.1308.2069 · pith_short_12: GFAO4QSUEV25 · pith_short_16: GFAO4QSUEV2536FB · pith_short_8: GFAO4QSU

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/GFAO4QSUEV2536FBMPCQC2P3QP \
  | 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: 3140ee42542575ddf8a163c50169fb83ee6de7a47a8e6e4e8affb958c2b6a0f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25aef9a096b76f021ad1d9c1e7f33c47fe5454fdff68bd5671e2073403beb4b1",
    "cross_cats_sorted": [
      "math.GR",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2013-08-09T09:55:25Z",
    "title_canon_sha256": "f0ceaa3037b8459e132deb4ee38c9443b6e675d211f2861545ecf2300bb1840a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.2069",
    "kind": "arxiv",
    "version": 1
  }
}