Pith Number

pith:E3EVBTD3

pith:2017:E3EVBTD3I7U4BMHU3I2LHIID46

not attested not anchored not stored refs pending

Lower Bounds for Betti Numbers of Monomial Ideals

Adam Boocher, James Seiner

arxiv:1706.09866 v1 · 2017-06-29 · 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{E3EVBTD3I7U4BMHU3I2LHIID46}

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	2026-05-18T00:41:13.640618Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26c950cc7b47e9c0b0f4da34b3a103e7994803a59eeba5f58c591ac9348e1e05

Aliases

arxiv: 1706.09866 · arxiv_version: 1706.09866v1 · doi: 10.48550/arxiv.1706.09866 · pith_short_12: E3EVBTD3I7U4 · pith_short_16: E3EVBTD3I7U4BMHU · pith_short_8: E3EVBTD3

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/E3EVBTD3I7U4BMHU3I2LHIID46 \
  | 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: 26c950cc7b47e9c0b0f4da34b3a103e7994803a59eeba5f58c591ac9348e1e05

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0dfdb993c1393da4a58fbe92dcf07601e5aab99089f9f7fcae55a1c36371032a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2017-06-29T17:28:36Z",
    "title_canon_sha256": "4017b9177f281556937374776df2452ae39414c37d0d63e7980f408fc7ce93cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.09866",
    "kind": "arxiv",
    "version": 1
  }
}