Pith Number

pith:PGLO3J7D

pith:2010:PGLO3J7DI2PUVMFLCAY3FLHW5B

not attested not anchored not stored refs pending

Z-Structures on Product Groups

Carrie J. Tirel

arxiv:1010.0284 v1 · 2010-10-02 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PGLO3J7DI2PUVMFLCAY3FLHW5B}

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	2026-05-18T01:22:29.246367Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7996eda7e3469f4ab0ab1031b2acf6e849c07c5f2dceca4939646d1c41dae223

Aliases

arxiv: 1010.0284 · arxiv_version: 1010.0284v1 · doi: 10.48550/arxiv.1010.0284 · pith_short_12: PGLO3J7DI2PU · pith_short_16: PGLO3J7DI2PUVMFL · pith_short_8: PGLO3J7D

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/PGLO3J7DI2PUVMFLCAY3FLHW5B \
  | 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: 7996eda7e3469f4ab0ab1031b2acf6e849c07c5f2dceca4939646d1c41dae223

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd895e809bcfa7719901a213959cdd81d79202653fc2165b154cf76be4a50b2e",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-10-02T01:27:13Z",
    "title_canon_sha256": "aaa2c09f3864408551bdef2ceccdf5eea312fc18a7d099e173816fc250d2c95c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.0284",
    "kind": "arxiv",
    "version": 1
  }
}