Pith Number

pith:C4U32GVI

pith:2016:C4U32GVIT7LNLX2I3QIVNW4YF6

not attested not anchored not stored refs pending

When are n-syzygy modules n-torsionfree?

Hiroki Matsui, Ryo Takahashi, Yoshinao Tsuchiya

arxiv:1604.03684 v1 · 2016-04-13 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C4U32GVIT7LNLX2I3QIVNW4YF6}

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	2026-05-18T01:17:11.934239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1729bd1aa89fd6d5df48dc1156db982f881b2782008a0136cbbde9a066472921

Aliases

arxiv: 1604.03684 · arxiv_version: 1604.03684v1 · doi: 10.48550/arxiv.1604.03684 · pith_short_12: C4U32GVIT7LN · pith_short_16: C4U32GVIT7LNLX2I · pith_short_8: C4U32GVI

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/C4U32GVIT7LNLX2I3QIVNW4YF6 \
  | 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: 1729bd1aa89fd6d5df48dc1156db982f881b2782008a0136cbbde9a066472921

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3dd75735e70bae47e5fadde605faef4409f3e9f40ec4741f7e0b7712f3a528a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-04-13T08:13:32Z",
    "title_canon_sha256": "bc98ec04a8ab4f5ef5cf3017407b89fdc804868678c832e903588798120363e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.03684",
    "kind": "arxiv",
    "version": 1
  }
}