Pith Number

pith:ATUTLKR4

pith:2012:ATUTLKR4YAIDD64JLM4S4U5YL6

not attested not anchored not stored refs pending

Geometric Sobolev-like embedding using high-dimensional Menger-like curvature

S{\l}awomir Kolasi\'nski

arxiv:1205.4112 v2 · 2012-05-18 · 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{ATUTLKR4YAIDD64JLM4S4U5YL6}

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	2026-05-18T01:26:50.722462Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04e935aa3cc01031fb895b392e53b85fbb74b81dcc659c5f81f9d877fb6baf45

Aliases

arxiv: 1205.4112 · arxiv_version: 1205.4112v2 · doi: 10.48550/arxiv.1205.4112 · pith_short_12: ATUTLKR4YAID · pith_short_16: ATUTLKR4YAIDD64J · pith_short_8: ATUTLKR4

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/ATUTLKR4YAIDD64JLM4S4U5YL6 \
  | 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: 04e935aa3cc01031fb895b392e53b85fbb74b81dcc659c5f81f9d877fb6baf45

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cea3cee10aa2d58bcf070d2e24a9e025f15b7e895bdacf7d084908a4a0d502d4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-05-18T08:35:17Z",
    "title_canon_sha256": "21caeb848b889878a67c98c1e3fab55720e7d2cadf3a6dae1e47673cfa4a59d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.4112",
    "kind": "arxiv",
    "version": 2
  }
}