Pith Number

pith:AXLXT5HA

pith:2009:AXLXT5HA25L7FPZMMUDPL6TUA2

not attested not anchored not stored refs pending

The congruence criterion for power operations in Morava E-theory

Charles Rezk

arxiv:0902.2499 v2 · 2009-02-14 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AXLXT5HA25L7FPZMMUDPL6TUA2}

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	2026-07-04T17:17:04.803693Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05d779f4e0d757f2bf2c6506f5fa740687778befe42e2ca382057aec742cfa06

Aliases

arxiv: 0902.2499 · arxiv_version: 0902.2499v2 · doi: 10.48550/arxiv.0902.2499 · pith_short_12: AXLXT5HA25L7 · pith_short_16: AXLXT5HA25L7FPZM · pith_short_8: AXLXT5HA

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/AXLXT5HA25L7FPZMMUDPL6TUA2 \
  | 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: 05d779f4e0d757f2bf2c6506f5fa740687778befe42e2ca382057aec742cfa06

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74a607ded01c5bd9f3acfb6f8a62e5b64bcce08eb491967eef62734dd012faf6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2009-02-14T22:24:53Z",
    "title_canon_sha256": "7aa810c4de0c22356e1ccd23246ae509b158f199ef66a4f30eab8cb3a1aa6be4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.2499",
    "kind": "arxiv",
    "version": 2
  }
}