Pith Number

pith:5XWI6LIO

pith:2019:5XWI6LIOYBFR6RWADY6XF3O43L

not attested not anchored not stored refs pending

On Gross-Keating's result of lifting endomorphisms for formal modules

Qirui Li

arxiv:1902.10789 v1 · 2019-02-27 · 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{5XWI6LIOYBFR6RWADY6XF3O43L}

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	2026-05-17T23:52:29.739307Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

edec8f2d0ec04b1f46c01e3d72eddcdae18ed14749003813b2229f46b2ef71e5

Aliases

arxiv: 1902.10789 · arxiv_version: 1902.10789v1 · doi: 10.48550/arxiv.1902.10789 · pith_short_12: 5XWI6LIOYBFR · pith_short_16: 5XWI6LIOYBFR6RWA · pith_short_8: 5XWI6LIO

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/5XWI6LIOYBFR6RWADY6XF3O43L \
  | 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: edec8f2d0ec04b1f46c01e3d72eddcdae18ed14749003813b2229f46b2ef71e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f1fe0a45a3cf8f64a20f0a3baa66526c3d818327c2a53ca8a49bb7d12b1fbef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-02-27T21:07:21Z",
    "title_canon_sha256": "6f57e44ba642b357fc8291af4893a1c9d9daed6fa7af9fbf8781dd38f0bdfd92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.10789",
    "kind": "arxiv",
    "version": 1
  }
}