Pith Number

pith:RYP5JXVM

pith:2026:RYP5JXVMGVFMG6IB5WTGL426EQ

not attested not anchored not stored refs pending

Follow the Mean: Reference-Guided Flow Matching

Floor Eijkelboom, Jan-Willem van de Meent, Maksim Zhdanov, Pedro M. P. Curvo

Flow matching admits controllable generation by shifting the conditional endpoint mean computed from a reference set, enabling training-free guidance on frozen pretrained models.

arxiv:2605.10302 v3 · 2026-05-11 · cs.LG

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\usepackage{pith}
\pithnumber{RYP5JXVMGVFMG6IB5WTGL426EQ}

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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.

Claims

C1strongest claim

For deterministic interpolants, the velocity field is solely governed by a conditional endpoint mean; shifting this mean shifts the flow itself.

C2weakest assumption

That the interpolants remain deterministic and that the endpoint mean fully determines the velocity field without additional dependencies on the reference distribution or noise schedule.

C3one line summary

Flow matching admits controllable generation by shifting the conditional endpoint mean computed from a reference set, enabling training-free guidance on frozen pretrained models.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-26T01:03:33.082486Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8e1fd4deac354ac37901eda665f35e2405876d6d4e9b3ae06eff581965a28bed

Aliases

arxiv: 2605.10302 · arxiv_version: 2605.10302v3 · doi: 10.48550/arxiv.2605.10302 · pith_short_12: RYP5JXVMGVFM · pith_short_16: RYP5JXVMGVFMG6IB · pith_short_8: RYP5JXVM

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/RYP5JXVMGVFMG6IB5WTGL426EQ \
  | 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: 8e1fd4deac354ac37901eda665f35e2405876d6d4e9b3ae06eff581965a28bed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df018ac408c8367a288012f3be36ccf92638529b58d33b3817431a343ec739e9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-11T09:57:34Z",
    "title_canon_sha256": "9c788d145bdd510cdaa959e54caba3f76f18dfaa3dc6fdad4c563512e1b906fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10302",
    "kind": "arxiv",
    "version": 3
  }
}