Pith Number

pith:2FF45KTX

pith:2012:2FF45KTX2LX4HL5LOAP6HCOQG4

not attested not anchored not stored refs pending

Upper and lower estimates for schauder frames and atomic decompositions

Daniel Freeman, Kevin Beanland, Rui Liu

arxiv:1202.2492 v1 · 2012-02-12 · 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{2FF45KTX2LX4HL5LOAP6HCOQG4}

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	2026-05-18T04:02:26.414354Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d14bceaa77d2efc3afab701fe389d037009dd450c7ce0f2fb916bf1ee41a152a

Aliases

arxiv: 1202.2492 · arxiv_version: 1202.2492v1 · doi: 10.48550/arxiv.1202.2492 · pith_short_12: 2FF45KTX2LX4 · pith_short_16: 2FF45KTX2LX4HL5L · pith_short_8: 2FF45KTX

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/2FF45KTX2LX4HL5LOAP6HCOQG4 \
  | 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: d14bceaa77d2efc3afab701fe389d037009dd450c7ce0f2fb916bf1ee41a152a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f878f4a27fbfbc02a422d94013e70473750d01972ceb1f67c417c9a0731a73e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-02-12T06:54:49Z",
    "title_canon_sha256": "6bb97bf7c53d6a1bcf172e25ec9c8103cfd717fd427567adf9c7bc769106ac4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.2492",
    "kind": "arxiv",
    "version": 1
  }
}