Pith Number

pith:JXXRGSQI

pith:2007:JXXRGSQI6ZMGTE3J7YKR5BVGBH

not attested not anchored not stored refs pending

On defect groups for generalized blocks of the symmetric group

Jean-Baptiste Gramain

arxiv:math/0703157 v2 · 2007-03-06 · math.RT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JXXRGSQI6ZMGTE3J7YKR5BVGBH}

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	2026-05-18T02:57:45.243701Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4def134a08f658699369fe151e86a609ec5940fe7107a8900bfb4cf95b016381

Aliases

arxiv: math/0703157 · arxiv_version: math/0703157v2 · doi: 10.48550/arxiv.math/0703157 · pith_short_12: JXXRGSQI6ZMG · pith_short_16: JXXRGSQI6ZMGTE3J · pith_short_8: JXXRGSQI

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/JXXRGSQI6ZMGTE3J7YKR5BVGBH \
  | 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: 4def134a08f658699369fe151e86a609ec5940fe7107a8900bfb4cf95b016381

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "caf27dac5f9cf7f2832c9375d2c84ebf9f1dc994e5c19a598e1df9a273f4dc8e",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.RT",
    "submitted_at": "2007-03-06T15:12:29Z",
    "title_canon_sha256": "7d14cfbc8d27ee2706600eb1717bee6c5c82cfd8e3563a88cb39f9ff9e31120a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703157",
    "kind": "arxiv",
    "version": 2
  }
}