Pith Number

pith:YU6FNLFM

pith:2015:YU6FNLFM6II4E3GXAZ44XYUGUI

not attested not anchored not stored refs pending

Singular Sets and the Lavrentiev Phenomenon

Richard Gratwick

arxiv:1503.06694 v1 · 2015-03-23 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YU6FNLFM6II4E3GXAZ44XYUGUI}

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	2026-05-17T23:40:14.643287Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c53c56acacf211c26cd70679cbe286a23d49e52dcdd015ed4a19d31bf2a6326f

Aliases

arxiv: 1503.06694 · arxiv_version: 1503.06694v1 · doi: 10.48550/arxiv.1503.06694 · pith_short_12: YU6FNLFM6II4 · pith_short_16: YU6FNLFM6II4E3GX · pith_short_8: YU6FNLFM

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/YU6FNLFM6II4E3GXAZ44XYUGUI \
  | 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: c53c56acacf211c26cd70679cbe286a23d49e52dcdd015ed4a19d31bf2a6326f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd11d91b64610c4aaa3740d9bcc4110f1b5d1d2978d4d1b6f0f8a61e4250b728",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-03-23T15:51:44Z",
    "title_canon_sha256": "97295d9d2770168d15439d063e99414181f8f06bc8dfbf1a91d41a0d121b1980"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.06694",
    "kind": "arxiv",
    "version": 1
  }
}