Pith Number

pith:WZLUU6MV

pith:2026:WZLUU6MVYOQGROQDAXKSZXF3SY

not attested not anchored not stored refs pending

Modularity of Higher Theta Series III: Proof of the Modularity Conjecture

Tony Feng, Wei Zhang, Zhiwei Yun

arxiv:2608.07173 v1 · 2026-08-07 · 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{WZLUU6MVYOQGROQDAXKSZXF3SY}

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	2026-08-10T01:14:31.571901Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6574a7995c3a068ba0305d52cdcbb961377e8d0f7b5e521e715e5be6d48120c

Aliases

arxiv: 2608.07173 · arxiv_version: 2608.07173v1 · doi: 10.48550/arxiv.2608.07173 · pith_short_12: WZLUU6MVYOQG · pith_short_16: WZLUU6MVYOQGROQD · pith_short_8: WZLUU6MV

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/WZLUU6MVYOQGROQDAXKSZXF3SY \
  | 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: b6574a7995c3a068ba0305d52cdcbb961377e8d0f7b5e521e715e5be6d48120c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0be819a7843146d057c1303bf83575efa320fbce3b0d971d51ab90b369bc7178",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-08-07T12:45:34Z",
    "title_canon_sha256": "66f12240d280f8c24b52d9b0b32dd84238f3f99cac1362819fc6816c518d243a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.07173",
    "kind": "arxiv",
    "version": 1
  }
}