Pith Number

pith:OFZEJBIY

pith:2018:OFZEJBIYUCVXIYN77TDTV3HBBY

not attested not anchored not stored refs pending

Embedding the Heisenberg group into a bounded dimensional Euclidean space with optimal distortion

Terence Tao

arxiv:1811.09223 v2 · 2018-11-22 · math.AP · 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{OFZEJBIYUCVXIYN77TDTV3HBBY}

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	2026-05-17T23:40:43.600397Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7172448518a0ab7461bffcc73aece10e14383d044c66840e7be25af404de5f33

Aliases

arxiv: 1811.09223 · arxiv_version: 1811.09223v2 · doi: 10.48550/arxiv.1811.09223 · pith_short_12: OFZEJBIYUCVX · pith_short_16: OFZEJBIYUCVXIYN7 · pith_short_8: OFZEJBIY

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/OFZEJBIYUCVXIYN77TDTV3HBBY \
  | 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: 7172448518a0ab7461bffcc73aece10e14383d044c66840e7be25af404de5f33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a26c9925fbc536d5ffcb6448879eb32c0f69f7bdfa8f2c915dd8e214ba9d0050",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-11-22T16:11:36Z",
    "title_canon_sha256": "e48fbd0678164531281be913ddc01c687d9e89175bd608f445d00f17221de577"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.09223",
    "kind": "arxiv",
    "version": 2
  }
}