Pith Number

pith:RJ7NQJB2

pith:2023:RJ7NQJB2TUGLJJNCXQSPYF3RLS

not attested not anchored not stored refs pending

Crystalline representations and Wach modules in the relative case II

Abhinandan

arxiv:2309.16446 v2 · 2023-09-28 · math.NT · 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{RJ7NQJB2TUGLJJNCXQSPYF3RLS}

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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.

Cited by

1 paper in Pith

Prismatic $F$-crystals and Wach modules

Receipt and verification

First computed	2026-06-19T16:11:07.773863Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a7ed8243a9d0cb4a5a2bc24fc17715cb7b1717b661d86d8840ae2045d30c4e5

Aliases

arxiv: 2309.16446 · arxiv_version: 2309.16446v2 · doi: 10.48550/arxiv.2309.16446 · pith_short_12: RJ7NQJB2TUGL · pith_short_16: RJ7NQJB2TUGLJJNC · pith_short_8: RJ7NQJB2

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/RJ7NQJB2TUGLJJNCXQSPYF3RLS \
  | 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: 8a7ed8243a9d0cb4a5a2bc24fc17715cb7b1717b661d86d8840ae2045d30c4e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a6097e8200ab414c3fb9857d3b7ef052370424263927fcbdcc7a7b90a32dba4",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2023-09-28T13:56:36Z",
    "title_canon_sha256": "30297a2aa127fbe5bedd513c6451498e3064f2a037784345255ed5e2cb29e120"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2309.16446",
    "kind": "arxiv",
    "version": 2
  }
}