Pith Number

pith:DYB3F2YR

pith:2007:DYB3F2YRKFEHDY7Q73TPPK54HH

not attested not anchored not stored refs pending

Upper bounds of Hilbert coefficients and Hilbert functions

Juan Elias

arxiv:0709.4084 v1 · 2007-09-26 · 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{DYB3F2YRKFEHDY7Q73TPPK54HH}

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	2026-05-17T23:47:21.373155Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e03b2eb11514871e3f0fee6f7abbc39cb4d2f1e86d081a0294ebdad59431a83

Aliases

arxiv: 0709.4084 · arxiv_version: 0709.4084v1 · doi: 10.48550/arxiv.0709.4084 · pith_short_12: DYB3F2YRKFEH · pith_short_16: DYB3F2YRKFEHDY7Q · pith_short_8: DYB3F2YR

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/DYB3F2YRKFEHDY7Q73TPPK54HH \
  | 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: 1e03b2eb11514871e3f0fee6f7abbc39cb4d2f1e86d081a0294ebdad59431a83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36ae586721c8680b891ec7918dcd368c8921ed43bcfb1a8d2c12bcc888845d9b",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AC",
    "submitted_at": "2007-09-26T06:18:05Z",
    "title_canon_sha256": "45411bdb9af332464dd5cce37e8403768685ec003340555bb03e07706d5cb2fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.4084",
    "kind": "arxiv",
    "version": 1
  }
}