Pith Number

pith:TVQH4W5X

pith:2026:TVQH4W5XVTZCHPZWMUH7K47GYN

not attested not anchored not stored refs pending

Frequency-Domain Multi-Modality Transportation Modeling

Boyuan Zhang, Hangchen Liu, Jiewen Deng, Junchen Li, Renhe Jiang

arxiv:2607.08475 v1 · 2026-07-09 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TVQH4W5XVTZCHPZWMUH7K47GYN}

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	2026-07-10T01:19:51.591794Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d607e5bb7acf223bf36650ff573e6c36d2d7ef688cc95c610271cd989d84ff8

Aliases

arxiv: 2607.08475 · arxiv_version: 2607.08475v1 · doi: 10.48550/arxiv.2607.08475 · pith_short_12: TVQH4W5XVTZC · pith_short_16: TVQH4W5XVTZCHPZW · pith_short_8: TVQH4W5X

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/TVQH4W5XVTZCHPZWMUH7K47GYN \
  | 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: 9d607e5bb7acf223bf36650ff573e6c36d2d7ef688cc95c610271cd989d84ff8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27fba2dee0406627f92e164e32ad1c60f8d76062789a4c567e485cd214ed8b8a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-09T13:30:42Z",
    "title_canon_sha256": "6e8e62be91cb8bec3ff2eb5a87f15dce84bdb945ff6f63753012c9bb237df25b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08475",
    "kind": "arxiv",
    "version": 1
  }
}