Pith Number

pith:ATILHH76

pith:2010:ATILHH76CTYI4KAISWQKVMNFTL

not attested not anchored not stored refs pending

Betti numbers of multigraded modules of generic type

Alexandre Tchernev, Hara Charalambous

arxiv:1004.5472 v1 · 2010-04-30 · 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{ATILHH76CTYI4KAISWQKVMNFTL}

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	2026-05-18T02:24:10.026552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04d0b39ffe14f08e280895a0aab1a59ae507b7beca4043e711f78c1370b15c60

Aliases

arxiv: 1004.5472 · arxiv_version: 1004.5472v1 · doi: 10.48550/arxiv.1004.5472 · pith_short_12: ATILHH76CTYI · pith_short_16: ATILHH76CTYI4KAI · pith_short_8: ATILHH76

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/ATILHH76CTYI4KAISWQKVMNFTL \
  | 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: 04d0b39ffe14f08e280895a0aab1a59ae507b7beca4043e711f78c1370b15c60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca4398ca0ad9e25d17934e60388f71262f7fec1cf56112dd8796580706fcdc84",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-04-30T08:51:28Z",
    "title_canon_sha256": "ceafe477868832572a3d5438da89aa530f79cacb2f8bfbad1144a40bfd912d44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.5472",
    "kind": "arxiv",
    "version": 1
  }
}