Pith Number

pith:BQ4U4U6K

pith:2009:BQ4U4U6KYLREXMUFE6QZFKWCBV

not attested not anchored not stored refs pending

Local constancy for the reduction mod p of 2-dimensional crystalline representations

Laurent Berger

arxiv:0907.0221 v2 · 2009-07-01 · 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{BQ4U4U6KYLREXMUFE6QZFKWCBV}

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	2026-05-18T02:58:03.000432Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c394e53cac2e24bb28527a192aac20d418bc05bd56554f4cd75499da59884ce

Aliases

arxiv: 0907.0221 · arxiv_version: 0907.0221v2 · doi: 10.48550/arxiv.0907.0221 · pith_short_12: BQ4U4U6KYLRE · pith_short_16: BQ4U4U6KYLREXMUF · pith_short_8: BQ4U4U6K

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/BQ4U4U6KYLREXMUFE6QZFKWCBV \
  | 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: 0c394e53cac2e24bb28527a192aac20d418bc05bd56554f4cd75499da59884ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4f9e9f82094b67f6312cced1686ac6522deab04d2abed57d13ad1c50d9e7fa9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-07-01T18:51:13Z",
    "title_canon_sha256": "fd073d17862721aa203371eedc156d04a3fff45467978789a7ce182659f1602d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.0221",
    "kind": "arxiv",
    "version": 2
  }
}