Pith Number

pith:GRWLWXSM

pith:2009:GRWLWXSMJQ7E43ZRTVAASAZSW6

not attested not anchored not stored refs pending

Galois Theory for H-extensions and H-coextensions

Dorota Marciniak, Marcin Szamotulski

arxiv:0912.1795 v7 · 2009-12-09 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GRWLWXSMJQ7E43ZRTVAASAZSW6}

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	2026-05-18T04:08:13.816682Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

346cbb5e4c4c3e4e6f319d40090332b794f052c763e8513cb6d2901417b58739

Aliases

arxiv: 0912.1795 · arxiv_version: 0912.1795v7 · doi: 10.48550/arxiv.0912.1795 · pith_short_12: GRWLWXSMJQ7E · pith_short_16: GRWLWXSMJQ7E43ZR · pith_short_8: GRWLWXSM

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/GRWLWXSMJQ7E43ZRTVAASAZSW6 \
  | 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: 346cbb5e4c4c3e4e6f319d40090332b794f052c763e8513cb6d2901417b58739

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a430ab100a3ed842287e52b89d30d486bb4dc43883e7a3d649a33286c8ab38a9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2009-12-09T17:06:29Z",
    "title_canon_sha256": "0f33986369047528d96f58272992172cf1284a6b17178e40c0374226789cf5c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.1795",
    "kind": "arxiv",
    "version": 7
  }
}