Pith Number

pith:JP6ER4E7

pith:2010:JP6ER4E7ELMJ7XLF6OGJAKCFRN

not attested not anchored not stored refs pending

Algebraic entropy of generalized shifts on direct products

Anna Giordano Bruno

arxiv:1006.5208 v1 · 2010-06-27 · 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{JP6ER4E7ELMJ7XLF6OGJAKCFRN}

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	2026-05-18T04:33:39.415679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bfc48f09f22d89fdd65f38c9028458b4b39de99e58dda585190e35c7024a389

Aliases

arxiv: 1006.5208 · arxiv_version: 1006.5208v1 · doi: 10.48550/arxiv.1006.5208 · pith_short_12: JP6ER4E7ELMJ · pith_short_16: JP6ER4E7ELMJ7XLF · pith_short_8: JP6ER4E7

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/JP6ER4E7ELMJ7XLF6OGJAKCFRN \
  | 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: 4bfc48f09f22d89fdd65f38c9028458b4b39de99e58dda585190e35c7024a389

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15185c9cd171fb949e3585039deb5991926667d3762808487a9503c8d51f7568",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-06-27T12:55:00Z",
    "title_canon_sha256": "302ac1f00651acd8cbed0d3339c2b3afee3cc9c2dd3deafd6cf4d7ebe8897b19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.5208",
    "kind": "arxiv",
    "version": 1
  }
}