Pith Number

pith:3KPV2MMY

pith:2003:3KPV2MMYQMDQQ4JS6UYLHCZ6GA

not attested not anchored not stored refs pending

Geodesic distances on density matrices

Anna Jencova

arxiv:math-ph/0312044 v1 · 2003-12-17 · math-ph · math.DG · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3KPV2MMYQMDQQ4JS6UYLHCZ6GA}

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	2026-05-18T01:38:33.611983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da9f5d31988307087132f530b38b3e301a02f3f2f236a739fa75588bb29665d6

Aliases

arxiv: math-ph/0312044 · arxiv_version: math-ph/0312044v1 · doi: 10.48550/arxiv.math-ph/0312044 · pith_short_12: 3KPV2MMYQMDQ · pith_short_16: 3KPV2MMYQMDQQ4JS · pith_short_8: 3KPV2MMY

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/3KPV2MMYQMDQQ4JS6UYLHCZ6GA \
  | 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: da9f5d31988307087132f530b38b3e301a02f3f2f236a739fa75588bb29665d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ef25240df75c4aee149411c55ac676598c47889cd0fa1725cddfacd8dbaed3f",
    "cross_cats_sorted": [
      "math.DG",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2003-12-17T12:59:35Z",
    "title_canon_sha256": "abe8ccff59fd7f8f75742a394ecc9471bf88885066ab6a38d5c2505b1947e3d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0312044",
    "kind": "arxiv",
    "version": 1
  }
}