Pith Number

pith:36PKT6XD

pith:2025:36PKT6XDXBCCWAHSQMWVQYG2EQ

not attested not anchored not stored refs pending

The entrywise calculus and dimension-free positivity preservers, with an Appendix on sphere packings

Apoorva Khare

arxiv:2511.08406 v2 · 2025-11-11 · math.CA · math.FA · math.MG · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{36PKT6XDXBCCWAHSQMWVQYG2EQ}

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	2026-05-25T02:01:09.289240Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df9ea9fae3b8442b00f2832d5860da242d8d10cb7bacc487c5e08426a1ffeee6

Aliases

arxiv: 2511.08406 · arxiv_version: 2511.08406v2 · doi: 10.48550/arxiv.2511.08406 · pith_short_12: 36PKT6XDXBCC · pith_short_16: 36PKT6XDXBCCWAHS · pith_short_8: 36PKT6XD

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/36PKT6XDXBCCWAHSQMWVQYG2EQ \
  | 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: df9ea9fae3b8442b00f2832d5860da242d8d10cb7bacc487c5e08426a1ffeee6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5db796177bdf425509ecb5f3d401a4614246b598a9eea38a7d29251c10e0021",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2025-11-11T16:22:18Z",
    "title_canon_sha256": "854b4a0b94de523120da2dbe71cfa8b216b857a6d42104b55ff98f39ac146517"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.08406",
    "kind": "arxiv",
    "version": 2
  }
}