Pith Number

pith:VNNUB42P

pith:2026:VNNUB42PJBJRQSVXJV2CNIUW7F

not attested not anchored not stored refs pending

Discrete analogues in harmonic analysis: $TT^*$ methods

Bartosz Langowski, Mariusz Mirek, Tomasz Z. Szarek

arxiv:2606.07359 v1 · 2026-06-05 · 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{VNNUB42PJBJRQSVXJV2CNIUW7F}

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	2026-06-08T01:05:21.952102Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab5b40f34f4853184ab74d7426a296f95ff044f31ec8feed6a87e1c2ffadd18b

Aliases

arxiv: 2606.07359 · arxiv_version: 2606.07359v1 · doi: 10.48550/arxiv.2606.07359 · pith_short_12: VNNUB42PJBJR · pith_short_16: VNNUB42PJBJRQSVX · pith_short_8: VNNUB42P

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/VNNUB42PJBJRQSVXJV2CNIUW7F \
  | 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: ab5b40f34f4853184ab74d7426a296f95ff044f31ec8feed6a87e1c2ffadd18b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9f11dd37ce528e71ea2ce663c3daa5c72e369bf5b4706f1c55013f14ef8faa1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2026-06-05T15:06:13Z",
    "title_canon_sha256": "5c811284e509c5a2b0f463a31b1c753474fb813cfd948afb044d8fca3806e582"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.07359",
    "kind": "arxiv",
    "version": 1
  }
}