Pith Number

pith:FDOBPYLJ

pith:2026:FDOBPYLJCGLI2KFUHPUC5QGBVV

not attested not anchored not stored refs pending

Betti-Whittaker periods under duality: variations and applications

A. Raghuram, Giancarlo Castellano, Nasit Darshan, Shih-Yu Chen

arxiv:2607.17617 v1 · 2026-07-20 · 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{FDOBPYLJCGLI2KFUHPUC5QGBVV}

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	2026-07-21T01:21:55.329546Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28dc17e16911968d28b43be82ec0c1ad625c70e8700efa4e7ae751edaf8d50e4

Aliases

arxiv: 2607.17617 · arxiv_version: 2607.17617v1 · doi: 10.48550/arxiv.2607.17617 · pith_short_12: FDOBPYLJCGLI · pith_short_16: FDOBPYLJCGLI2KFU · pith_short_8: FDOBPYLJ

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/FDOBPYLJCGLI2KFUHPUC5QGBVV \
  | 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: 28dc17e16911968d28b43be82ec0c1ad625c70e8700efa4e7ae751edaf8d50e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77204139eee1c66454fb37cc2c55129c471bc8c5c51b7094bfb1e4614e1d741d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-20T07:11:46Z",
    "title_canon_sha256": "75a06e6f36b178664d501e6021e2ceef2f77fd95876177cfe42036109b1a55c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.17617",
    "kind": "arxiv",
    "version": 1
  }
}