Pith Number

pith:ZABQK6K4

pith:2016:ZABQK6K4YV2K4EUTDGSV7TZMT5

not attested not anchored not stored refs pending

Coupling in the Heisenberg group and its applications to gradient estimates

Maria Gordina, Phanuel Mariano, Sayan Banerjee

arxiv:1610.06430 v3 · 2016-10-20 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZABQK6K4YV2K4EUTDGSV7TZMT5}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T00:29:41.004455Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c80305795cc574ae129319a55fcf2c9f40a4ab76d6f0f6407f70ac43f0c8bb82

Aliases

arxiv: 1610.06430 · arxiv_version: 1610.06430v3 · doi: 10.48550/arxiv.1610.06430 · pith_short_12: ZABQK6K4YV2K · pith_short_16: ZABQK6K4YV2K4EUT · pith_short_8: ZABQK6K4

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/ZABQK6K4YV2K4EUTDGSV7TZMT5 \
  | 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: c80305795cc574ae129319a55fcf2c9f40a4ab76d6f0f6407f70ac43f0c8bb82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a0659e1e1ba970a616d5b4725c8ee11354754adf30b8e8c86e00dcbf3d8800a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-10-20T14:29:51Z",
    "title_canon_sha256": "2127e36ec3151a40ce4a21aa40f4f51abb0553a3c82c301744967d5999e4f612"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.06430",
    "kind": "arxiv",
    "version": 3
  }
}