Pith Number

pith:Q34KPBHD

pith:2020:Q34KPBHDDMUWJZ3RGD3BRQIHP3

not attested not anchored not stored refs pending

On the $K_4$ group of modular curves

Fran\c{c}ois Brunault

arxiv:2009.07614 v3 · 2020-09-16 · math.NT · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q34KPBHDDMUWJZ3RGD3BRQIHP3}

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.

Cited by

1 paper in Pith

Elements in $K_4$ and regulator maps of Fermat curves

Receipt and verification

First computed	2026-07-05T12:01:50.927376Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86f8a784e31b2964e77130f618c1077ec60a1a723518e4408583334820f62051

Aliases

arxiv: 2009.07614 · arxiv_version: 2009.07614v3 · doi: 10.48550/arxiv.2009.07614 · pith_short_12: Q34KPBHDDMUW · pith_short_16: Q34KPBHDDMUWJZ3R · pith_short_8: Q34KPBHD

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/Q34KPBHDDMUWJZ3RGD3BRQIHP3 \
  | 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: 86f8a784e31b2964e77130f618c1077ec60a1a723518e4408583334820f62051

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2313c53421834f3dc39207289b79cbd4528b28de5dd32d2f01d87759ff51dd0a",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2020-09-16T11:46:18Z",
    "title_canon_sha256": "107c7317ee766e273cb9558fc725ce04937648c83c8531d58ede9fd80c075069"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2009.07614",
    "kind": "arxiv",
    "version": 3
  }
}