Pith Number

pith:ZCQ7I4BV

pith:2019:ZCQ7I4BV7VTFVWTVP5YMQAVLTA

not attested not anchored not stored refs pending

Wach models and overconvergence of \'etale $(\varphi, \Gamma)$-modules

Hui Gao

arxiv:1906.09117 v1 · 2019-06-20 · 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{ZCQ7I4BV7VTFVWTVP5YMQAVLTA}

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	2026-05-17T23:42:44.482689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8a1f47035fd665ada757f70c802ab9838887aaaf03d24add23f1472cc51ac9b

Aliases

arxiv: 1906.09117 · arxiv_version: 1906.09117v1 · doi: 10.48550/arxiv.1906.09117 · pith_short_12: ZCQ7I4BV7VTF · pith_short_16: ZCQ7I4BV7VTFVWTV · pith_short_8: ZCQ7I4BV

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/ZCQ7I4BV7VTFVWTVP5YMQAVLTA \
  | 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: c8a1f47035fd665ada757f70c802ab9838887aaaf03d24add23f1472cc51ac9b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f0b53123bd8f8202446243fe6920243b37f33cc754d6993228b8826d288a1b5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-06-20T07:54:53Z",
    "title_canon_sha256": "ddb6eb2c2c3471a848a7ffc5300fbdafc296718e1635be9046e62bb00cb26029"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.09117",
    "kind": "arxiv",
    "version": 1
  }
}