Pith Number

pith:IRVDWY2E

pith:2012:IRVDWY2ED4ALGUZJB4KT76TDH7

not attested not anchored not stored refs pending

Trace theorems: critical cases and best constants

Michael Ruzhansky, Mitsuru Sugimoto

arxiv:1208.3200 v1 · 2012-08-15 · math.FA · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IRVDWY2ED4ALGUZJB4KT76TDH7}

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	2026-05-18T02:30:32.825893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

446a3b63441f00b353290f153ffa633ff19715010533413fd8f7d5a100b6781d

Aliases

arxiv: 1208.3200 · arxiv_version: 1208.3200v1 · doi: 10.48550/arxiv.1208.3200 · pith_short_12: IRVDWY2ED4AL · pith_short_16: IRVDWY2ED4ALGUZJ · pith_short_8: IRVDWY2E

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/IRVDWY2ED4ALGUZJB4KT76TDH7 \
  | 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: 446a3b63441f00b353290f153ffa633ff19715010533413fd8f7d5a100b6781d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d37844fa7881d4a0ab49b561ee7f23607bffcafb4cfbb3fa71756f568c6bee7e",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-08-15T20:00:27Z",
    "title_canon_sha256": "ea403fe21d1a5180414bd8e0da5a97a9a90ac31a32e9e84c883cc8534be34893"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3200",
    "kind": "arxiv",
    "version": 1
  }
}