Pith Number

pith:PVKW5ACE

pith:2018:PVKW5ACEPWB6HN37SPKTZINDKS

not attested not anchored not stored refs pending

Difference hierarchies and duality with an application to formal languages

Andreas Krebs, C\'elia Borlido, Howard Straubing, Mai Gehrke

arxiv:1812.01921 v1 · 2018-12-05 · math.GN · cs.FL · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PVKW5ACEPWB6HN37SPKTZINDKS}

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	2026-05-17T23:59:00.248747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d556e80447d83e3b77f93d53ca1a35494dd9af6e7c4351257756b564172cf47

Aliases

arxiv: 1812.01921 · arxiv_version: 1812.01921v1 · doi: 10.48550/arxiv.1812.01921 · pith_short_12: PVKW5ACEPWB6 · pith_short_16: PVKW5ACEPWB6HN37 · pith_short_8: PVKW5ACE

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/PVKW5ACEPWB6HN37SPKTZINDKS \
  | 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: 7d556e80447d83e3b77f93d53ca1a35494dd9af6e7c4351257756b564172cf47

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59d50afcee1e556fc4d70ef2ed27ebfdf8037d0f78aeaf68103b28fc35351ae2",
    "cross_cats_sorted": [
      "cs.FL",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2018-12-05T11:22:26Z",
    "title_canon_sha256": "e48eb77019981020b1744063ce6cee9058f5b8fd9abf724ce3c5e6d03a0607c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.01921",
    "kind": "arxiv",
    "version": 1
  }
}