Pith Number

pith:J5GZA535

pith:1993:J5GZA535FV54OYO7LUTO3Y566F

not attested not anchored not stored refs pending

Proportional subspaces of spaces with unconditional basis have good volume properties

Marius Junge

arxiv:math/9312208 v1 · 1993-12-29 · 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{J5GZA535FV54OYO7LUTO3Y566F}

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	2026-05-18T01:05:51.762284Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f4d90777d2d7bc761df5d26ede3bef166dfcb62072ccd8c3dc1043311299a3a

Aliases

arxiv: math/9312208 · arxiv_version: math/9312208v1 · doi: 10.48550/arxiv.math/9312208 · pith_short_12: J5GZA535FV54 · pith_short_16: J5GZA535FV54OYO7 · pith_short_8: J5GZA535

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/J5GZA535FV54OYO7LUTO3Y566F \
  | 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: 4f4d90777d2d7bc761df5d26ede3bef166dfcb62072ccd8c3dc1043311299a3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e12cb90938b6db992df9832bb3185790a826437c44fa09c769fddbc27012fd97",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "1993-12-29T17:04:17Z",
    "title_canon_sha256": "7a5a095a34b3891adbd6094a2d50c5c0ee12ed74df4eeaf094d4139998755b9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9312208",
    "kind": "arxiv",
    "version": 1
  }
}