Pith Number

pith:3MZFYMGS

pith:2019:3MZFYMGSQKOA6YEI4UZBJAGFT3

not attested not anchored not stored refs pending

Relative deformation theory, relative Selmer groups, and lifting irreducible Galois representations

Chandrashekhar Khare, Najmuddin Fakhruddin, Stefan Patrikis

arxiv:1904.02374 v5 · 2019-04-04 · 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{3MZFYMGSQKOA6YEI4UZBJAGFT3}

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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.

Cited by

1 paper in Pith

Lifting $G$-irreducible but $\mathrm{GL}_n$-reducible Galois representations

Receipt and verification

First computed	2026-07-05T03:22:56.690194Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db325c30d2829c0f6088e5321480c59ecbfdf6bc09cb2d0c0e501c7513a9f31d

Aliases

arxiv: 1904.02374 · arxiv_version: 1904.02374v5 · doi: 10.48550/arxiv.1904.02374 · pith_short_12: 3MZFYMGSQKOA · pith_short_16: 3MZFYMGSQKOA6YEI · pith_short_8: 3MZFYMGS

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/3MZFYMGSQKOA6YEI4UZBJAGFT3 \
  | 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: db325c30d2829c0f6088e5321480c59ecbfdf6bc09cb2d0c0e501c7513a9f31d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6959197e6bd2d85a283be6c509a1613061e5b8479d472f6ddbd8b7518d3fbea3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-04-04T06:49:37Z",
    "title_canon_sha256": "56af1b555c111914a3d3a9c61dcc9eef47b0bfde3e4f253b0aaf421645cd569f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.02374",
    "kind": "arxiv",
    "version": 5
  }
}