Pith Number

pith:AZF4YYRP

pith:2014:AZF4YYRP43G3DOGIYCWZUHHE5L

not attested not anchored not stored refs pending

Toeplitz Corona and the Douglas Property for Free Functions

Sriram Balasubramanian

arxiv:1411.1965 v1 · 2014-11-07 · 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{AZF4YYRP43G3DOGIYCWZUHHE5L}

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	2026-05-18T02:38:20.049737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

064bcc622fe6cdb1b8c8c0ad9a1ce4eaf80741667aa22eb44c2df24c1775bcd9

Aliases

arxiv: 1411.1965 · arxiv_version: 1411.1965v1 · doi: 10.48550/arxiv.1411.1965 · pith_short_12: AZF4YYRP43G3 · pith_short_16: AZF4YYRP43G3DOGI · pith_short_8: AZF4YYRP

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/AZF4YYRP43G3DOGIYCWZUHHE5L \
  | 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: 064bcc622fe6cdb1b8c8c0ad9a1ce4eaf80741667aa22eb44c2df24c1775bcd9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2699532c0a7e74f82faca56101128982959a2314bab93908b4bc496f649f6d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-11-07T16:32:56Z",
    "title_canon_sha256": "5a9773e945c28192622bc8e8e85a8248c78a44fb2ee184dbfbf9581a8ba87166"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.1965",
    "kind": "arxiv",
    "version": 1
  }
}