Pith Number

pith:OTOTZVPT

pith:2018:OTOTZVPTBTOSAI74BQP7CHMJO5

not attested not anchored not stored refs pending

Bi-Lipschitz embeddings of Heisenberg submanifolds into Euclidean spaces

Scott Zimmerman, Sean Li, Vasileios Chousionis, Vyron Vellis

arxiv:1812.07612 v1 · 2018-12-18 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OTOTZVPTBTOSAI74BQP7CHMJO5}

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	2026-05-17T23:57:56.559999Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74dd3cd5f30cdd2023fc0c1ff11d89777618893e3c646fa8031f929cbd5194cb

Aliases

arxiv: 1812.07612 · arxiv_version: 1812.07612v1 · doi: 10.48550/arxiv.1812.07612 · pith_short_12: OTOTZVPTBTOS · pith_short_16: OTOTZVPTBTOSAI74 · pith_short_8: OTOTZVPT

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/OTOTZVPTBTOSAI74BQP7CHMJO5 \
  | 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: 74dd3cd5f30cdd2023fc0c1ff11d89777618893e3c646fa8031f929cbd5194cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "660d0b4e292f04c6972539839a0067ac5128c9a69400d486d2fdfa5a78ce055f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2018-12-18T19:29:52Z",
    "title_canon_sha256": "057c62571f014b2b94b147ff47b18e5bdc8c8fff0b61f776048c284d14aee619"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.07612",
    "kind": "arxiv",
    "version": 1
  }
}