Pith Number

pith:MIY2J6PG

pith:2016:MIY2J6PGSJP3EIXU3Z2FOYHCTH

not attested not anchored not stored refs pending

Closedness and invertibility for the sum of two closed operators

Nikolaos Roidos

arxiv:1602.04465 v2 · 2016-02-14 · 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{MIY2J6PGSJP3EIXU3Z2FOYHCTH}

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	2026-05-18T00:16:56.903646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6231a4f9e6925fb222f4de745760e299dd319ff5d6d7a0d1cfa3ef9f8b774755

Aliases

arxiv: 1602.04465 · arxiv_version: 1602.04465v2 · doi: 10.48550/arxiv.1602.04465 · pith_short_12: MIY2J6PGSJP3 · pith_short_16: MIY2J6PGSJP3EIXU · pith_short_8: MIY2J6PG

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/MIY2J6PGSJP3EIXU3Z2FOYHCTH \
  | 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: 6231a4f9e6925fb222f4de745760e299dd319ff5d6d7a0d1cfa3ef9f8b774755

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ece1b8bd4b2d7608d9a2337c38641474c9c05b3a28972f15a87f86bcb626bae5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-02-14T15:27:26Z",
    "title_canon_sha256": "9204ba64dd2ba6fb24925ee78bd44b3abe554c89a4ebb3a34c8311c490b74f8a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.04465",
    "kind": "arxiv",
    "version": 2
  }
}