Pith Number

pith:TLFTFQL4

pith:2011:TLFTFQL4OK62X6TIVRPKTGSRHC

not attested not anchored not stored refs pending

Jacobian hits circuits: Hitting-sets, lower bounds for depth-D occur-k formulas & depth-3 transcendence degree-k circuits

Chandan Saha, Manindra Agrawal, Nitin Saxena, Ramprasad Saptharishi

arxiv:1111.0582 v1 · 2011-11-02 · cs.CC · 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{TLFTFQL4OK62X6TIVRPKTGSRHC}

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	2026-05-18T04:09:44.653937Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9acb32c17c72bdabfa68ac5ea99a5138902518ce4cfba62cbc2f9b644104f4da

Aliases

arxiv: 1111.0582 · arxiv_version: 1111.0582v1 · doi: 10.48550/arxiv.1111.0582 · pith_short_12: TLFTFQL4OK62 · pith_short_16: TLFTFQL4OK62X6TI · pith_short_8: TLFTFQL4

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/TLFTFQL4OK62X6TIVRPKTGSRHC \
  | 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: 9acb32c17c72bdabfa68ac5ea99a5138902518ce4cfba62cbc2f9b644104f4da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c119c960a545d58b3f2a6c18b8fc122786007ac373bbec38cc1cd59fd876d19e",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2011-11-02T17:52:45Z",
    "title_canon_sha256": "2dc9be4cc97a3c2821b9bc073d57d9adac80850f4c9a86b754acb28f36529741"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0582",
    "kind": "arxiv",
    "version": 1
  }
}