Pith Number

pith:GECUSYOH

pith:2015:GECUSYOH4ZDHBIUNEYZRE24BBL

not attested not anchored not stored refs pending

A note on crystalline liftings in the $\mathbb{Q}_p$ case

Hui Gao

arxiv:1505.00125 v2 · 2015-05-01 · 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{GECUSYOH4ZDHBIUNEYZRE24BBL}

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	2026-05-17T23:45:47.147216Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31054961c7e64670a28d2633126b810ae000c8356a064611a3a7705edab27dc3

Aliases

arxiv: 1505.00125 · arxiv_version: 1505.00125v2 · doi: 10.48550/arxiv.1505.00125 · pith_short_12: GECUSYOH4ZDH · pith_short_16: GECUSYOH4ZDHBIUN · pith_short_8: GECUSYOH

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/GECUSYOH4ZDHBIUNEYZRE24BBL \
  | 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: 31054961c7e64670a28d2633126b810ae000c8356a064611a3a7705edab27dc3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11db6ccd5937894a4c88f8c43f23a4e31c0cfa755a31c82ced7c6c06501e5d16",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-05-01T08:53:18Z",
    "title_canon_sha256": "d9ba6c1d64b54e4eafff2235077b42ab5894a342495c62908818b670ef51a7d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.00125",
    "kind": "arxiv",
    "version": 2
  }
}