Pith Number

pith:4IDO2H4O

pith:2013:4IDO2H4OH2J5DCYZXIGH7TAOQG

not attested not anchored not stored refs pending

Multivariable $(\varphi,\Gamma)$-modules and locally analytic vectors

Laurent Berger

arxiv:1312.4753 v8 · 2013-12-17 · math.NT · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4IDO2H4OH2J5DCYZXIGH7TAOQG}

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	2026-05-18T00:50:23.631046Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e206ed1f8e3e93d18b19ba0c7fcc0e818ff5fef088dea17c7ba645c7259961c0

Aliases

arxiv: 1312.4753 · arxiv_version: 1312.4753v8 · doi: 10.48550/arxiv.1312.4753 · pith_short_12: 4IDO2H4OH2J5 · pith_short_16: 4IDO2H4OH2J5DCYZ · pith_short_8: 4IDO2H4O

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/4IDO2H4OH2J5DCYZXIGH7TAOQG \
  | 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: e206ed1f8e3e93d18b19ba0c7fcc0e818ff5fef088dea17c7ba645c7259961c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2fe268ff8f408ee8be6e2ac2a0be3e5eb943bb658ebac655d07163d5f4b37aa",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-12-17T12:41:51Z",
    "title_canon_sha256": "a203c70b4e9cef8daa3a079dc14e8eed163643d0a4d4e037919ecf24fb116efd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.4753",
    "kind": "arxiv",
    "version": 8
  }
}