Pith Number

pith:6MPGTIUD

pith:2015:6MPGTIUDSA5OH55U47NWU4S7O5

not attested not anchored not stored refs pending

The Hadamard product and the free convolutions

Arijit Chakrabarty

arxiv:1511.03770 v1 · 2015-11-12 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6MPGTIUDSA5OH55U47NWU4S7O5}

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	2026-05-18T01:27:06.826348Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f31e69a283903ae3f7b4e7db6a725f777130cf74c430444ac13bf1833c0b854f

Aliases

arxiv: 1511.03770 · arxiv_version: 1511.03770v1 · doi: 10.48550/arxiv.1511.03770 · pith_short_12: 6MPGTIUDSA5O · pith_short_16: 6MPGTIUDSA5OH55U · pith_short_8: 6MPGTIUD

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/6MPGTIUDSA5OH55U47NWU4S7O5 \
  | 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: f31e69a283903ae3f7b4e7db6a725f777130cf74c430444ac13bf1833c0b854f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a1a4e64b04b667ad7694a48da0fdfa77221ee4b49c79c11ed8355e521da1605",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-11-12T04:28:46Z",
    "title_canon_sha256": "e8a1d39090198049cb1a107465ed3a6153cba34bd0b96635c1717e9d8ee686c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.03770",
    "kind": "arxiv",
    "version": 1
  }
}