Pith Number

pith:VDKN4HVV

pith:2018:VDKN4HVVLOA3YLILD7QPTCKJNY

not attested not anchored not stored refs pending

Some aspects of number theory related to phase operators

F. Bouzeffour, M. Garayev

arxiv:1812.03486 v2 · 2018-12-09 · math.FA · math-ph · math.MP · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VDKN4HVVLOA3YLILD7QPTCKJNY}

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	2026-05-17T23:57:30.613763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8d4de1eb55b81bc2d0b1fe0f989496e363b8d6a08bab0b5f85ace77de902594

Aliases

arxiv: 1812.03486 · arxiv_version: 1812.03486v2 · doi: 10.48550/arxiv.1812.03486 · pith_short_12: VDKN4HVVLOA3 · pith_short_16: VDKN4HVVLOA3YLIL · pith_short_8: VDKN4HVV

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/VDKN4HVVLOA3YLILD7QPTCKJNY \
  | 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: a8d4de1eb55b81bc2d0b1fe0f989496e363b8d6a08bab0b5f85ace77de902594

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94218cb565400fd0815e6be922fde733bd2f7964223136b3beda1246705e4041",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-12-09T13:32:26Z",
    "title_canon_sha256": "03a064da47505d4976fa97f958ded7288205d3699b57e421adcdcdf518a543f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.03486",
    "kind": "arxiv",
    "version": 2
  }
}