Pith Number

pith:FD5TNHRF

pith:2014:FD5TNHRF3UZA3VZIXZGEKZUXXS

not attested not anchored not stored refs pending

The Sarason Sub-Symbol and the Recovery of the Symbol of Densely Defined Toeplitz Operators over the Hardy Space

Joel Rosenfeld

arxiv:1412.5969 v1 · 2014-12-18 · 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{FD5TNHRF3UZA3VZIXZGEKZUXXS}

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	2026-05-18T02:30:55.852769Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28fb369e25dd320dd728be4c456697bc8464374b4d74ae49d2bbe6ab4dc45098

Aliases

arxiv: 1412.5969 · arxiv_version: 1412.5969v1 · doi: 10.48550/arxiv.1412.5969 · pith_short_12: FD5TNHRF3UZA · pith_short_16: FD5TNHRF3UZA3VZI · pith_short_8: FD5TNHRF

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/FD5TNHRF3UZA3VZIXZGEKZUXXS \
  | 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: 28fb369e25dd320dd728be4c456697bc8464374b4d74ae49d2bbe6ab4dc45098

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e5eac732ed76f1277eb16885272644a68407d00a1ad66a3e0220ac3db163c4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-12-18T17:49:30Z",
    "title_canon_sha256": "8df9ce11316ea4c5f245ea736e9383dd9071e8669574dc6455c1d57ac41525fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.5969",
    "kind": "arxiv",
    "version": 1
  }
}