Pith Number

pith:XZKO4I7L

pith:2026:XZKO4I7LOKMPH52I2735BM3Q6P

not attested not anchored not stored refs pending

Euler systems and the symmetric square of a Hida family

Debanjana Kundu, Jishnu Ray, Stefano Vigni

arxiv:2607.12679 v1 · 2026-07-14 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XZKO4I7LOKMPH52I2735BM3Q6P}

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	2026-07-15T01:22:11.667233Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be54ee23eb7298f3f748d7f7d0b370f3f634acfda1050a25fdb34066a3f36acc

Aliases

arxiv: 2607.12679 · arxiv_version: 2607.12679v1 · doi: 10.48550/arxiv.2607.12679 · pith_short_12: XZKO4I7LOKMP · pith_short_16: XZKO4I7LOKMPH52I · pith_short_8: XZKO4I7L

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/XZKO4I7LOKMPH52I2735BM3Q6P \
  | 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: be54ee23eb7298f3f748d7f7d0b370f3f634acfda1050a25fdb34066a3f36acc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63e4f7cb3e4b636e5117a6486d0bdf22294d961a74cdea2414868762a516cdcd",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-14T12:08:10Z",
    "title_canon_sha256": "8dabca35f256b42eee9f3b875ec5d3b9fae997d46f9dd83ac0619fe127cdbba8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.12679",
    "kind": "arxiv",
    "version": 1
  }
}