Pith Number

pith:4IXPECG4

pith:2012:4IXPECG4PDK2L3BIVVPNNMQLXV

not attested not anchored not stored refs pending

Duplex numbers, diffusion systems, and generalized quantum mechanics

Jerzy Kocik

arxiv:1201.3069 v1 · 2012-01-15 · 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{4IXPECG4PDK2L3BIVVPNNMQLXV}

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	2026-05-18T04:04:32.330232Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e22ef208dc78d5a5ec28ad5ed6b20bbd762d2e73b14e355464e023eac2aa3940

Aliases

arxiv: 1201.3069 · arxiv_version: 1201.3069v1 · doi: 10.48550/arxiv.1201.3069 · pith_short_12: 4IXPECG4PDK2 · pith_short_16: 4IXPECG4PDK2L3BI · pith_short_8: 4IXPECG4

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/4IXPECG4PDK2L3BIVVPNNMQLXV \
  | 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: e22ef208dc78d5a5ec28ad5ed6b20bbd762d2e73b14e355464e023eac2aa3940

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9df91e675c1a384dd583f3f4706e99ed85da72d57a5813214ed7d88813fe916",
    "cross_cats_sorted": [
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-01-15T08:52:41Z",
    "title_canon_sha256": "9aeac8f19d3b349444fabf45597856eee343a9892b6bdbe1025ca18c09008f71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.3069",
    "kind": "arxiv",
    "version": 1
  }
}