Pith Number

pith:LXGCCA3Q

pith:2019:LXGCCA3QWHBAEGUPYOW3J5KC24

not attested not anchored not stored refs pending

The Group Theoretic Roots of Information: permutations, symmetry, and entropy

David J. Galas

arxiv:1908.09642 v2 · 2019-08-23 · cs.IT · 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{LXGCCA3QWHBAEGUPYOW3J5KC24}

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	2026-07-05T00:21:14.591671Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5dcc210370b1c2021a8fc3adb4f542d73241c627d999ad0ab6fd3b4554638b08

Aliases

arxiv: 1908.09642 · arxiv_version: 1908.09642v2 · doi: 10.48550/arxiv.1908.09642 · pith_short_12: LXGCCA3QWHBA · pith_short_16: LXGCCA3QWHBAEGUP · pith_short_8: LXGCCA3Q

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/LXGCCA3QWHBAEGUPYOW3J5KC24 \
  | 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: 5dcc210370b1c2021a8fc3adb4f542d73241c627d999ad0ab6fd3b4554638b08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71b433661bbe6e0819fcd2e90be35c3b595f644c0b394db9f77a41b381cc4cdb",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2019-08-23T17:05:49Z",
    "title_canon_sha256": "8a2bb948f3942cc4ce3a592a504a4480afa3af14cd9e44cbb90fedacdd7bdc4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.09642",
    "kind": "arxiv",
    "version": 2
  }
}