Pith Number

pith:DLSQXIXM

pith:2006:DLSQXIXMN4TTJKUAGEXL57MNVI

not attested not anchored not stored refs pending

Sobolev mappings: Lipschitz density is not a bi-Lipschitz invariant of the target

Piotr Hajlasz

arxiv:math/0602029 v1 · 2006-02-01 · 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{DLSQXIXMN4TTJKUAGEXL57MNVI}

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	2026-05-18T04:12:34.249556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ae50ba2ec6f2734aa80312ebefd8daa095b648e71f7a68065a6707b45d6987b

Aliases

arxiv: math/0602029 · arxiv_version: math/0602029v1 · doi: 10.48550/arxiv.math/0602029 · pith_short_12: DLSQXIXMN4TT · pith_short_16: DLSQXIXMN4TTJKUA · pith_short_8: DLSQXIXM

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/DLSQXIXMN4TTJKUAGEXL57MNVI \
  | 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: 1ae50ba2ec6f2734aa80312ebefd8daa095b648e71f7a68065a6707b45d6987b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e396caa1529ea21a2c993b97b0daef40191db1cc5df5d65f7cbae842e35760f0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2006-02-01T20:37:07Z",
    "title_canon_sha256": "494210b33cf58828fb6f3da0aaa098e93e88a2b54beb25e6c8716a6d5a002331"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0602029",
    "kind": "arxiv",
    "version": 1
  }
}