Pith Number

pith:3LBKQAKW

pith:2017:3LBKQAKW4TD5NAORNXHHMPZKRC

not attested not anchored not stored refs pending

Summability properties of Gabor expansions

Alexander Borichev, Anton Baranov, Yurii Belov

arxiv:1706.05685 v2 · 2017-06-18 · math.CV · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3LBKQAKW4TD5NAORNXHHMPZKRC}

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	2026-05-17T23:59:03.738578Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dac2a80156e4c7d681d16dce763f2a88af56cd975bb0307c88b2219d765f6144

Aliases

arxiv: 1706.05685 · arxiv_version: 1706.05685v2 · doi: 10.48550/arxiv.1706.05685 · pith_short_12: 3LBKQAKW4TD5 · pith_short_16: 3LBKQAKW4TD5NAOR · pith_short_8: 3LBKQAKW

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/3LBKQAKW4TD5NAORNXHHMPZKRC \
  | 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: dac2a80156e4c7d681d16dce763f2a88af56cd975bb0307c88b2219d765f6144

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ab6ef20e763379515bf1b20cbed30c037ad5d53a579792c61e8d3ba0d37c68c",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2017-06-18T16:37:19Z",
    "title_canon_sha256": "a6824e17fe6c1ebc605156d059707000457437db40b7fc664adf0932e7c4f587"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.05685",
    "kind": "arxiv",
    "version": 2
  }
}