Pith Number

pith:N6IUGHF7

pith:2011:N6IUGHF7ZV5KCU3RCQSO3M3TQC

not attested not anchored not stored refs pending

Cartier duality for $(\phi, \hat{G})$-modules

Yoshiyasu Ozeki

arxiv:1105.5477 v1 · 2011-05-27 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N6IUGHF7ZV5KCU3RCQSO3M3TQC}

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	2026-05-18T04:21:11.597020Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f91431cbfcd7aa153711424edb37380a943a0221c7b2465ea5fce582b41cf68

Aliases

arxiv: 1105.5477 · arxiv_version: 1105.5477v1 · doi: 10.48550/arxiv.1105.5477 · pith_short_12: N6IUGHF7ZV5K · pith_short_16: N6IUGHF7ZV5KCU3R · pith_short_8: N6IUGHF7

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/N6IUGHF7ZV5KCU3RCQSO3M3TQC \
  | 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: 6f91431cbfcd7aa153711424edb37380a943a0221c7b2465ea5fce582b41cf68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ff5acc495767e0814e344d5e7be433b0cf5885615b713286eec114d8ae5e194",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-05-27T04:54:57Z",
    "title_canon_sha256": "ea7f49ecb5616b204dbbcfd6f34fe8d501591c9bbeb6d1cc1fea64e661a90b3d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5477",
    "kind": "arxiv",
    "version": 1
  }
}