Pith Number

pith:46QL4S54

pith:2016:46QL4S54UCOMI5MVSDMM2B6OQE

not attested not anchored not stored refs pending

Loose crystalline lifts and overconvergence of \'etale $(\varphi, \tau)$-modules

Hui Gao, Tong Liu

arxiv:1606.07216 v3 · 2016-06-23 · 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{46QL4S54UCOMI5MVSDMM2B6OQE}

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	2026-05-18T00:21:37.863261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7a0be4bbca09cc4759590d8cd07ce812e70caf777989c28ff272850fe9f8239

Aliases

arxiv: 1606.07216 · arxiv_version: 1606.07216v3 · doi: 10.48550/arxiv.1606.07216 · pith_short_12: 46QL4S54UCOM · pith_short_16: 46QL4S54UCOMI5MV · pith_short_8: 46QL4S54

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/46QL4S54UCOMI5MVSDMM2B6OQE \
  | 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: e7a0be4bbca09cc4759590d8cd07ce812e70caf777989c28ff272850fe9f8239

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af58b43df08f6bbd67675d3d81ec6287d6ea05ca48dccac105b3056c1ff2d6bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-06-23T07:34:53Z",
    "title_canon_sha256": "a2117d84e610a28850c50ed6fa7632f6a98976578d656d70bae2866a4db3bd75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.07216",
    "kind": "arxiv",
    "version": 3
  }
}