Pith Number

pith:IBRUC3SG

pith:2012:IBRUC3SGD5F2O6O5XMMAUB3I7M

not attested not anchored not stored refs pending

Competition between phytoplankton and bacteria: exclusion and coexistence

Eric Beno\^it (MIA), Fr\'ed\'eric Grognard (INRIA Sophia Antipolis), Olivier Bernard (INRIA Sophia Antipolis), Pierre Masci (INRIA Sophia Antipolis)

arxiv:1208.0316 v2 · 2012-08-01 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IBRUC3SGD5F2O6O5XMMAUB3I7M}

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	2026-05-18T03:49:11.464411Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4063416e461f4ba779ddbb180a0768fb1e0c3081a2a3998cbb6085cbeb2cee61

Aliases

arxiv: 1208.0316 · arxiv_version: 1208.0316v2 · doi: 10.48550/arxiv.1208.0316 · pith_short_12: IBRUC3SGD5F2 · pith_short_16: IBRUC3SGD5F2O6O5 · pith_short_8: IBRUC3SG

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/IBRUC3SGD5F2O6O5XMMAUB3I7M \
  | 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: 4063416e461f4ba779ddbb180a0768fb1e0c3081a2a3998cbb6085cbeb2cee61

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85a38f9ace1d6bd2e40fcba2f5879568bdc2de0573dc582f4ff9694c04c53f5b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-08-01T18:44:13Z",
    "title_canon_sha256": "887df5381a242e8a07f13cb31dae5dac9166cdd023e9c91928e3e31b7c3c1ab2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.0316",
    "kind": "arxiv",
    "version": 2
  }
}