Pith Number

pith:UTHU6LNH

pith:2024:UTHU6LNHOEVFVTER3DYR6QQILG

not attested not anchored not stored refs pending

On the injective dimension of unit Cartier and Frobenius modules

Alexandria Wheeler, Daniel Fink, Manuel Blickle, Wenliang Zhang

arxiv:2412.08423 v1 · 2024-12-11 · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UTHU6LNHOEVFVTER3DYR6QQILG}

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	2026-07-05T09:47:49.932938Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4cf4f2da7712a5acc91d8f11f420859ad9e85f216cd3774e889ffb62b3b25fb

Aliases

arxiv: 2412.08423 · arxiv_version: 2412.08423v1 · doi: 10.48550/arxiv.2412.08423 · pith_short_12: UTHU6LNHOEVF · pith_short_16: UTHU6LNHOEVFVTER · pith_short_8: UTHU6LNH

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/UTHU6LNHOEVFVTER3DYR6QQILG \
  | 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: a4cf4f2da7712a5acc91d8f11f420859ad9e85f216cd3774e889ffb62b3b25fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4543cee0d51f5e383caabd7bab2235687783702a337339dfa6c616abedffb8fa",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2024-12-11T14:43:06Z",
    "title_canon_sha256": "278042e0b0fea870bd080f277d1e4a55ffdbbf0872dff1bfe57f30c8361f3ea0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.08423",
    "kind": "arxiv",
    "version": 1
  }
}