Pith Number

pith:UJLWMHY4

pith:2026:UJLWMHY4XPDGZNQVEUAO5AH55V

not attested not anchored not stored refs pending

Tree Coordinates and Range Martingales for Positive Operator-Valued Measures

James Tian

arxiv:2607.03924 v1 · 2026-07-04 · math.PR · math-ph · math.FA · 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{UJLWMHY4XPDGZNQVEUAO5AH55V}

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	2026-07-07T02:18:14.844288Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a257661f1cbbc66cb6152500ee80fded6ab1f57f72ba20d2cb77c93e41a26e2d

Aliases

arxiv: 2607.03924 · arxiv_version: 2607.03924v1 · doi: 10.48550/arxiv.2607.03924 · pith_short_12: UJLWMHY4XPDG · pith_short_16: UJLWMHY4XPDGZNQV · pith_short_8: UJLWMHY4

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/UJLWMHY4XPDGZNQVEUAO5AH55V \
  | 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: a257661f1cbbc66cb6152500ee80fded6ab1f57f72ba20d2cb77c93e41a26e2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19c2c86fdc4fd3fd76bfb75138c6b61f01a6dfa50e3f3189657ae5a40c678ad1",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-04T15:36:32Z",
    "title_canon_sha256": "e560055cb9523c4412ad377a5090d5682edde16be7de0867cef0e4f43af94636"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.03924",
    "kind": "arxiv",
    "version": 1
  }
}