Pith Number

pith:I2FAX36R

pith:2015:I2FAX36R7DU2FEG6FWFXONMLHJ

not attested not anchored not stored refs pending

D-functions and immanants of unitary matrices and submatrices

Dylan Spivak, Hubert de Guise, Ish Dhand, Justin Kulp

arxiv:1511.01851 v2 · 2015-11-05 · math-ph · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I2FAX36R7DU2FEG6FWFXONMLHJ}

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	2026-05-18T01:22:10.091252Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

468a0befd1f8e9a290de2d8b77358b3a42b3906b8e0a791b67cc086687b59f72

Aliases

arxiv: 1511.01851 · arxiv_version: 1511.01851v2 · doi: 10.48550/arxiv.1511.01851 · pith_short_12: I2FAX36R7DU2 · pith_short_16: I2FAX36R7DU2FEG6 · pith_short_8: I2FAX36R

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/I2FAX36R7DU2FEG6FWFXONMLHJ \
  | 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: 468a0befd1f8e9a290de2d8b77358b3a42b3906b8e0a791b67cc086687b59f72

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0bd738aba9c882f7bc1cdb3f17b5c342e8da66dbcc40bcd358051e026481230",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-11-05T18:47:31Z",
    "title_canon_sha256": "c85d30acc592876af8d2ffb7c3364ac41e40b967b52017172b0696a6e8409d70"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.01851",
    "kind": "arxiv",
    "version": 2
  }
}