Pith Number

pith:GMCOC7NW

pith:2019:GMCOC7NWSGABTGUAWEML3ETC6V

not attested not anchored not stored refs pending

Reductions of some two-dimensional crystalline representations via Kisin modules

Brandon Levin, John Bergdall

arxiv:1908.09036 v3 · 2019-08-23 · 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{GMCOC7NWSGABTGUAWEML3ETC6V}

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	2026-07-05T01:23:22.217597Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3304e17db69180199a80b118bd9262f544560124c45cc51a4f88dfbf87019c0a

Aliases

arxiv: 1908.09036 · arxiv_version: 1908.09036v3 · doi: 10.48550/arxiv.1908.09036 · pith_short_12: GMCOC7NWSGAB · pith_short_16: GMCOC7NWSGABTGUA · pith_short_8: GMCOC7NW

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/GMCOC7NWSGABTGUAWEML3ETC6V \
  | 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: 3304e17db69180199a80b118bd9262f544560124c45cc51a4f88dfbf87019c0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bee1df820be3da666ceba8a262d6bbe7cce1dfa9304ef61adad4a092cffcdf66",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-08-23T20:55:11Z",
    "title_canon_sha256": "2467faa5d286b1305f023ee451f8c2e878d31e63ad20c5b5a0d388dba480e789"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.09036",
    "kind": "arxiv",
    "version": 3
  }
}