Pith Number

pith:VGNH62VJ

pith:2015:VGNH62VJCD5R5E5VPAWNBLGNTH

not attested not anchored not stored refs pending

On the sum of a narrow and a compact operators

Volodymyr Mykhaylyuk

arxiv:1512.07838 v1 · 2015-12-23 · math.FA · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VGNH62VJCD5R5E5VPAWNBLGNTH}

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	2026-05-18T01:23:47.673959Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a99a7f6aa910fb1e93b5782cd0accd99da0991ab44745b16e60a691ed92227ac

Aliases

arxiv: 1512.07838 · arxiv_version: 1512.07838v1 · doi: 10.48550/arxiv.1512.07838 · pith_short_12: VGNH62VJCD5R · pith_short_16: VGNH62VJCD5R5E5V · pith_short_8: VGNH62VJ

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/VGNH62VJCD5R5E5VPAWNBLGNTH \
  | 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: a99a7f6aa910fb1e93b5782cd0accd99da0991ab44745b16e60a691ed92227ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e3639f5e9347207e30dc889d7d78ce4bcd2651548c53c65b0f7fa5102d978b9",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-12-23T14:08:10Z",
    "title_canon_sha256": "9b1717b527c4eb06dd578e79e9902df29cfff9793aa6c42da1557260cd622475"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07838",
    "kind": "arxiv",
    "version": 1
  }
}