Pith Number

pith:6VXTCCQL

pith:2012:6VXTCCQL6R6CMDV325DJDJUXWW

not attested not anchored not stored refs pending

Forced gradings and the Humphreys-Verma conjecture

Brian Parshall, Leonard Scott

arxiv:1212.0021 v1 · 2012-11-30 · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6VXTCCQL6R6CMDV325DJDJUXWW}

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	2026-05-18T03:39:27.630659Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f56f310a0bf47c260ebbd74691a697b5ac5d98a728f9299eeefb8341401fda23

Aliases

arxiv: 1212.0021 · arxiv_version: 1212.0021v1 · doi: 10.48550/arxiv.1212.0021 · pith_short_12: 6VXTCCQL6R6C · pith_short_16: 6VXTCCQL6R6CMDV3 · pith_short_8: 6VXTCCQL

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/6VXTCCQL6R6CMDV325DJDJUXWW \
  | 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: f56f310a0bf47c260ebbd74691a697b5ac5d98a728f9299eeefb8341401fda23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1f806df96f107e498c56e68e5a03defdf7ed15bdd6703dc4a8c407eb0e00472",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2012-11-30T21:51:03Z",
    "title_canon_sha256": "27220e141e6174fd23c54b01163c691417b312c20cdd01e812fb839bf384b313"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0021",
    "kind": "arxiv",
    "version": 1
  }
}