Pith Number

pith:KFZ3CEZU

pith:2021:KFZ3CEZU5H7TNCNGOYM5KUYWGS

not attested not anchored not stored refs pending

Iwasawa-Greenberg main conjecture for non-ordinary modular forms and Eisenstein congruences on $\mathrm{GU}(3,1)$

Francesc Castella, Xin Wan, Zheng Liu

arxiv:2109.08375 v1 · 2021-09-17 · 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{KFZ3CEZU5H7TNCNGOYM5KUYWGS}

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	2026-07-05T03:15:15.215376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5173b11334e9ff3689a67619d5531634b0f08cef682839f29e30c53ee859b46c

Aliases

arxiv: 2109.08375 · arxiv_version: 2109.08375v1 · doi: 10.48550/arxiv.2109.08375 · pith_short_12: KFZ3CEZU5H7T · pith_short_16: KFZ3CEZU5H7TNCNG · pith_short_8: KFZ3CEZU

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/KFZ3CEZU5H7TNCNGOYM5KUYWGS \
  | 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: 5173b11334e9ff3689a67619d5531634b0f08cef682839f29e30c53ee859b46c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8b087d209b40a3eac1631eceab5aaef271bf9ab74d62767c16d4a9851915e2c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-09-17T07:16:17Z",
    "title_canon_sha256": "d2bf603b682a9458c393f0f07a97544b78ab7ed22a91ba22d86d5ce5f33bd726"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.08375",
    "kind": "arxiv",
    "version": 1
  }
}