Pith Number

pith:YRKQ4DTY

pith:2015:YRKQ4DTYYBDGTGDSWMRCKDQKJB

not attested not anchored not stored refs pending

Harnack and Shmul'yan pre-order relations for Hilbert space contractions

Catalin Badea, Laurian Suciu

arxiv:1512.01990 v3 · 2015-12-07 · 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{YRKQ4DTYYBDGTGDSWMRCKDQKJB}

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	2026-05-18T00:14:23.208510Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4550e0e78c046699872b322250e0a4861d6fe34ed15bdd53636ff7310d9f6bc

Aliases

arxiv: 1512.01990 · arxiv_version: 1512.01990v3 · doi: 10.48550/arxiv.1512.01990 · pith_short_12: YRKQ4DTYYBDG · pith_short_16: YRKQ4DTYYBDGTGDS · pith_short_8: YRKQ4DTY

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/YRKQ4DTYYBDGTGDSWMRCKDQKJB \
  | 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: c4550e0e78c046699872b322250e0a4861d6fe34ed15bdd53636ff7310d9f6bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5bc38db25198bb640bdb436594207005bde23855172b94080c29b5e45316fc9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-12-07T11:39:32Z",
    "title_canon_sha256": "0cea35ed4372b6cd1e3ddf900757488a4e99cb023e7445f6a7ed5fb583b3cb71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.01990",
    "kind": "arxiv",
    "version": 3
  }
}