Pith Number

pith:4SM34425

pith:1999:4SM34425OL6GM2WDEWCNQJXGJC

not attested not anchored not stored refs pending

The quantum duality principle

Fabio Gavarini

arxiv:math/9909071 v8 · 1999-09-14 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4SM34425OL6GM2WDEWCNQJXGJC}

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	2026-05-18T00:43:03.502600Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e499be735d72fc666ac32584d826e64881d85342aa3e106e0dd8ea29b832f068

Aliases

arxiv: math/9909071 · arxiv_version: math/9909071v8 · doi: 10.48550/arxiv.math/9909071 · pith_short_12: 4SM34425OL6G · pith_short_16: 4SM34425OL6GM2WD · pith_short_8: 4SM34425

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/4SM34425OL6GM2WDEWCNQJXGJC \
  | 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: e499be735d72fc666ac32584d826e64881d85342aa3e106e0dd8ea29b832f068

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1fd8b4e2dd390224145d5e648b253c536cd6e877c2ca369aabbdcf599065172b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "1999-09-14T13:45:12Z",
    "title_canon_sha256": "24e78bc7688033804ec53e0f97a7214437b4f9c867af0c57b319bf2bf5491e85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9909071",
    "kind": "arxiv",
    "version": 8
  }
}