Pith Number

pith:VPFM6FBK

pith:2012:VPFM6FBKEV2TS435W4F66UV6JT

not attested not anchored not stored refs pending

The Brenner-Hochster-Koll\'ar and Whitney Problems for Vector-valued Functions and Jets

Charles L. Fefferman, Garving K. Luli

arxiv:1209.2449 v2 · 2012-09-11 · math.AG · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VPFM6FBKEV2TS435W4F66UV6JT}

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	2026-05-18T03:45:31.277995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abcacf142a257539737db70bef52be4cd3a64d1888c8aa22f29a4575d719beb4

Aliases

arxiv: 1209.2449 · arxiv_version: 1209.2449v2 · doi: 10.48550/arxiv.1209.2449 · pith_short_12: VPFM6FBKEV2T · pith_short_16: VPFM6FBKEV2TS435 · pith_short_8: VPFM6FBK

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/VPFM6FBKEV2TS435W4F66UV6JT \
  | 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: abcacf142a257539737db70bef52be4cd3a64d1888c8aa22f29a4575d719beb4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4618f1353870321af61b8668edbfdaf909cb35150b8437debcd74d97c0a6c6d7",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-09-11T21:56:19Z",
    "title_canon_sha256": "c402bc688f7169d8e4e693cd9aaa5318854a618caca527b7535c6c0d45e162cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2449",
    "kind": "arxiv",
    "version": 2
  }
}