Pith Number

pith:QRHD6UN7

pith:2026:QRHD6UN7GACBGKE6ZB4MMTKAN7

not attested not anchored not stored refs pending

Multi-Parameter Exponential Sums with Product Hilbert Kernels

Hoyoung Song, Joonil Kim

arxiv:2607.25955 v1 · 2026-07-28 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QRHD6UN7GACBGKE6ZB4MMTKAN7}

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	2026-07-29T01:26:12.962881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

844e3f51bf300413289ec878c64d406fe938aebad731a002bac1360c6b03e1c9

Aliases

arxiv: 2607.25955 · arxiv_version: 2607.25955v1 · doi: 10.48550/arxiv.2607.25955 · pith_short_12: QRHD6UN7GACB · pith_short_16: QRHD6UN7GACBGKE6 · pith_short_8: QRHD6UN7

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/QRHD6UN7GACBGKE6ZB4MMTKAN7 \
  | 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: 844e3f51bf300413289ec878c64d406fe938aebad731a002bac1360c6b03e1c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e7e64e813ec458927d0d75d0abd1d4f7237fb9d6ab12ed3249a639f8902d36e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-07-28T16:41:33Z",
    "title_canon_sha256": "40681fd8573071f44eeda79594983b234987bfaaba22223e9d4e148f0b0b3833"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.25955",
    "kind": "arxiv",
    "version": 1
  }
}