Pith Number

pith:L5YWRQRT

pith:2025:L5YWRQRT4C3EPEYBRSI2PODFMU

not attested not anchored not stored refs pending

A short proof of the existence of the injective envelope of an operator space

Thomas Sinclair

arxiv:2507.10931 v1 · 2025-07-15 · math.OA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L5YWRQRT4C3EPEYBRSI2PODFMU}

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	2026-07-05T11:37:28.672004Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f7168c233e0b64793018c91a7b8656524c964a8b642a41367031553a98dddb8

Aliases

arxiv: 2507.10931 · arxiv_version: 2507.10931v1 · doi: 10.48550/arxiv.2507.10931 · pith_short_12: L5YWRQRT4C3E · pith_short_16: L5YWRQRT4C3EPEYB · pith_short_8: L5YWRQRT

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/L5YWRQRT4C3EPEYBRSI2PODFMU \
  | 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: 5f7168c233e0b64793018c91a7b8656524c964a8b642a41367031553a98dddb8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b581064b8176c160a121aa2137f626ed37b5e20d2eac089ca27c576c91774575",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2025-07-15T02:49:10Z",
    "title_canon_sha256": "df697891ca69ba07e4d67c5ecaa05f3948505e3afcbc4dd131dc36a6321f5cb6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.10931",
    "kind": "arxiv",
    "version": 1
  }
}