Pith Number

pith:HO73YOSA

pith:2021:HO73YOSAQO5JXBU3J4LJ67QVUJ

not attested not anchored not stored refs pending

Dynamics on the number of prime divisors for additive arithmetic semigroups

Biao Wang

arxiv:2109.11290 v3 · 2021-09-23 · math.NT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HO73YOSAQO5JXBU3J4LJ67QVUJ}

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	2026-06-09T01:05:02.089210Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3bbfbc3a4083ba9b869b4f169f7e15a246dcbbe8264b3afe9e7a57c22a9afdf2

Aliases

arxiv: 2109.11290 · arxiv_version: 2109.11290v3 · doi: 10.48550/arxiv.2109.11290 · pith_short_12: HO73YOSAQO5J · pith_short_16: HO73YOSAQO5JXBU3 · pith_short_8: HO73YOSA

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/HO73YOSAQO5JXBU3J4LJ67QVUJ \
  | 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: 3bbfbc3a4083ba9b869b4f169f7e15a246dcbbe8264b3afe9e7a57c22a9afdf2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9962d2a3ccce1f89a5f44fe68b300f679d19a88f0e41642c39af041510d288da",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-09-23T10:54:23Z",
    "title_canon_sha256": "56fe788d440d90a5e14d6e48dd693db05bf4365c149f5d68584f34ae96c07812"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.11290",
    "kind": "arxiv",
    "version": 3
  }
}