Pith Number

pith:TPWZWHF3

pith:2014:TPWZWHF35T22XERRBA2QQECBYD

not attested not anchored not stored refs pending

Duality for generic algebras

Anders Kock

arxiv:1412.6660 v1 · 2014-12-20 · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TPWZWHF35T22XERRBA2QQECBYD}

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.

Cited by

2 papers in Pith

Constructive higher sheaf models with applications to synthetic mathematics

Receipt and verification

First computed	2026-05-18T02:30:46.489260Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bed9b1cbbecf5ab92310835081041c0f3318d8385aa3aae3aead7fdecb311c4

Aliases

arxiv: 1412.6660 · arxiv_version: 1412.6660v1 · doi: 10.48550/arxiv.1412.6660 · pith_short_12: TPWZWHF35T22 · pith_short_16: TPWZWHF35T22XERR · pith_short_8: TPWZWHF3

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/TPWZWHF35T22XERRBA2QQECBYD \
  | 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: 9bed9b1cbbecf5ab92310835081041c0f3318d8385aa3aae3aead7fdecb311c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b1d34cb5e75079b6603c8a5a71aa8cac2c4ba9308a2673f1a09d9c150602c1e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2014-12-20T15:14:10Z",
    "title_canon_sha256": "c2d7b0bc62fc9a0bbdf6404eaa6fbfa1adc46db1bdb881153396e749e92a70bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.6660",
    "kind": "arxiv",
    "version": 1
  }
}