Pith Number

pith:ROAWJ2BP

pith:2015:ROAWJ2BPG2B7U6UYWC3AXMPU7W

not attested not anchored not stored refs pending

Hilbert series and degree bounds for matrix (semi-)invariants

Visu Makam

arxiv:1510.08420 v1 · 2015-10-28 · math.RT · math.AC · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ROAWJ2BPG2B7U6UYWC3AXMPU7W}

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	2026-05-18T01:28:35.996359Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b8164e82f3683fa7a98b0b60bb1f4fdab1201d4ea053fc7811eb780b98f6039

Aliases

arxiv: 1510.08420 · arxiv_version: 1510.08420v1 · doi: 10.48550/arxiv.1510.08420 · pith_short_12: ROAWJ2BPG2B7 · pith_short_16: ROAWJ2BPG2B7U6UY · pith_short_8: ROAWJ2BP

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/ROAWJ2BPG2B7U6UYWC3AXMPU7W \
  | 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: 8b8164e82f3683fa7a98b0b60bb1f4fdab1201d4ea053fc7811eb780b98f6039

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b988602c27eafb215b71b1eed863259eeb254b5b2a3b5336c1fca0a40e59b794",
    "cross_cats_sorted": [
      "math.AC",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2015-10-28T19:06:47Z",
    "title_canon_sha256": "a8c374aa5c538e79a6f7183135bc66d585d13cb68ce5a6487b760d06471c7552"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.08420",
    "kind": "arxiv",
    "version": 1
  }
}