Pith Number

pith:VBZV77JU

pith:2019:VBZV77JUK64EXT52W36Q7WA2OC

not attested not anchored not stored refs pending

An indefinite range inclusion theorem for triplets of bounded linear operators on a Hilbert space

Atsushi Uchiyama, Michio Seto

arxiv:1901.06774 v2 · 2019-01-21 · 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{VBZV77JUK64EXT52W36Q7WA2OC}

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	2026-05-17T23:55:38.075261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8735ffd3457b84bcfbab6fd0fd81a709c1e08b509438cd167bcd42c94809dda

Aliases

arxiv: 1901.06774 · arxiv_version: 1901.06774v2 · doi: 10.48550/arxiv.1901.06774 · pith_short_12: VBZV77JUK64E · pith_short_16: VBZV77JUK64EXT52 · pith_short_8: VBZV77JU

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/VBZV77JUK64EXT52W36Q7WA2OC \
  | 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: a8735ffd3457b84bcfbab6fd0fd81a709c1e08b509438cd167bcd42c94809dda

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df95064f85fb2d2cf6a1dba5d039c310b75830bd1bcd09af2f3369b892e19e45",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-01-21T02:54:42Z",
    "title_canon_sha256": "fb76973f0ab27fb9e62fb6a814869a4ab6faeb08621535238d08b3a496215f67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.06774",
    "kind": "arxiv",
    "version": 2
  }
}