Pith Number

pith:3FBMD3JL

pith:2013:3FBMD3JLYXB2UVYJXJNN546SOA

not attested not anchored not stored refs pending

Langlands correspondence for isocrystals and the existence of crystalline companions for curves

Tomoyuki Abe

arxiv:1310.0528 v3 · 2013-10-02 · math.AG · 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{3FBMD3JLYXB2UVYJXJNN546SOA}

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	2026-05-18T00:19:04.891521Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d942c1ed2bc5c3aa5709ba5adef3d270008a9c57425bf81172e5c29270e16a82

Aliases

arxiv: 1310.0528 · arxiv_version: 1310.0528v3 · doi: 10.48550/arxiv.1310.0528 · pith_short_12: 3FBMD3JLYXB2 · pith_short_16: 3FBMD3JLYXB2UVYJ · pith_short_8: 3FBMD3JL

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/3FBMD3JLYXB2UVYJXJNN546SOA \
  | 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: d942c1ed2bc5c3aa5709ba5adef3d270008a9c57425bf81172e5c29270e16a82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b61ef1ffd05c6096b3de4987ebd1718b329b9d8c3c0e01d1dc36f724aeb0943",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-10-02T00:17:52Z",
    "title_canon_sha256": "66f9a3a8d2fa683d3fad2df3e465e54997bbdf89cf39b434e75277147a96e04a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.0528",
    "kind": "arxiv",
    "version": 3
  }
}