Pith Number

pith:T3TWYF3U

pith:2026:T3TWYF3UJTRWRX2IV24YEBH7BM

not attested not anchored not stored refs pending

Hankel and Multiplication Tensor Completions for Cactus Rank

Alessandra Bernardi, Joachim Jelisiejew, Oriol Reig Fit\'e

arxiv:2606.30600 v1 · 2026-06-29 · 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{T3TWYF3UJTRWRX2IV24YEBH7BM}

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	2026-06-30T02:18:22.244502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ee76c17744ce368df48aeb98204ff0b1620353484933eb7bf3e91f6193e91e1

Aliases

arxiv: 2606.30600 · arxiv_version: 2606.30600v1 · doi: 10.48550/arxiv.2606.30600 · pith_short_12: T3TWYF3UJTRW · pith_short_16: T3TWYF3UJTRWRX2I · pith_short_8: T3TWYF3U

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/T3TWYF3UJTRWRX2IV24YEBH7BM \
  | 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: 9ee76c17744ce368df48aeb98204ff0b1620353484933eb7bf3e91f6193e91e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50873b1e2d90fd80d61e33075f2d61de5f196dd49313534d9df2c4c62d3a2909",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2026-06-29T17:39:30Z",
    "title_canon_sha256": "6626741439f00aaf90eaaa31b4e1c7d77a78f5136db244ce8fb1d144dd6fa7c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30600",
    "kind": "arxiv",
    "version": 1
  }
}