Pith Number

pith:PP4K36DO

pith:2026:PP4K36DO532ZLVC7QUNE3ZVATO

not attested not anchored not stored refs pending

On estimating operator norm distance, with optimal trace distance estimation when one state is pure

Qisheng Wang, Yupan Liu, Zhan Yu

arxiv:2607.03905 v1 · 2026-07-04 · quant-ph · cs.DS · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PP4K36DO532ZLVC7QUNE3ZVATO}

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	2026-07-07T02:18:13.879700Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bf8adf86eeef595d45f851a4de6a09bb9a1592d4627506419b058e3998d3f75

Aliases

arxiv: 2607.03905 · arxiv_version: 2607.03905v1 · doi: 10.48550/arxiv.2607.03905 · pith_short_12: PP4K36DO532Z · pith_short_16: PP4K36DO532ZLVC7 · pith_short_8: PP4K36DO

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/PP4K36DO532ZLVC7QUNE3ZVATO \
  | 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: 7bf8adf86eeef595d45f851a4de6a09bb9a1592d4627506419b058e3998d3f75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b7a9638b070d25f7691367939ad9c7756204f12d2f6e196871ffbca7621d6597",
    "cross_cats_sorted": [
      "cs.DS",
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-04T14:59:03Z",
    "title_canon_sha256": "a47a021739c08ea6331ca5066606c0e6c69489d6a10969f03dec7ec3da6de8ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.03905",
    "kind": "arxiv",
    "version": 1
  }
}