Pith Number

pith:22EAOIPS

pith:2002:22EAOIPSZPF5H2OPEHC6JPIFZQ

not attested not anchored not stored refs pending

On isomorphisms between deformation rings and Hecke rings

Chandrashekhar Khare

arxiv:math/0211005 v1 · 2002-11-01 · 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{22EAOIPSZPF5H2OPEHC6JPIFZQ}

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	2026-05-18T01:38:29.357116Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6880721f2cbcbd3e9cf21c5e4bd05cc2b15b78c4cc933acdba06cb95375e1bb

Aliases

arxiv: math/0211005 · arxiv_version: math/0211005v1 · doi: 10.48550/arxiv.math/0211005 · pith_short_12: 22EAOIPSZPF5 · pith_short_16: 22EAOIPSZPF5H2OP · pith_short_8: 22EAOIPS

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/22EAOIPSZPF5H2OPEHC6JPIFZQ \
  | 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: d6880721f2cbcbd3e9cf21c5e4bd05cc2b15b78c4cc933acdba06cb95375e1bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "348ca711fb6da269bcd4969f9a5db662495a035512189aae4b9187a45b5675f1",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2002-11-01T00:13:28Z",
    "title_canon_sha256": "b5c7fc479b096f352830e7687813e5bc879452dd85c87425680dcfd9226d8ab2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0211005",
    "kind": "arxiv",
    "version": 1
  }
}