{"_canonicalization":{"envelope_id":"axm_ + sha256(envelope minus {signature, axiom_id, anchors})","envelope_signature":"ed25519(envelope minus {signature, axiom_id})","json":"sort_keys=True, separators=(',',':'), ensure_ascii=False, allow_nan=False, utf-8","leaf_hash":"sha256(0x00 || canonical_json(envelope_full))","seal_signature":"ed25519(seal minus {signature, sig_algorithm})"},"axiom_id":"axm_9040c4bf787d5cd98613b4311c7aa6dee05ef3d867e9b40cf8090e1d5be0aaeb","bitcoin_anchor":{"bitcoin_attestations":[],"calendar_attestations":[],"ots_url":"","stamped_at":"","status":"pending_next_stamp"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_9040c4bf787d5cd98613b4311c7aa6dee05ef3d867e9b40cf8090e1d5be0aaeb","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"7b2abb5620bea417b8d15e0ec1523b825c1ddfb4f85dc13b986856a9acf5d943","published":"Mon, 01 Jun 2026 00:00:00 -0400","receipt_hash":"7b2abb5620bea417b8d15e0ec1523b825c1ddfb4f85dc13b986856a9acf5d943","schema":"spider.news.vendor_press.v1","spider":"vendor_press","spider_record":{"axiom_subtype":"news.vendor_press.v1","category":"news","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"7b2abb5620bea417b8d15e0ec1523b825c1ddfb4f85dc13b986856a9acf5d943","observed_at":"2026-06-01T04:43:13.859018Z","parent_run_hash":"8993bbc535dae8c9669e099af3624cb39166b8d9bbfd66f26ae5c338cbb21be2","published":"Mon, 01 Jun 2026 00:00:00 -0400","runtime_version":"0.1.0","schema":"spider.news.vendor_press.v1","source_status":200,"source_url":"https://export.arxiv.org/rss/cs.AI","spider":"vendor_press","summary_excerpt":"arXiv:2602.07928v2 Announce Type: replace-cross \nAbstract: Flow-based generative models can be viewed through a physics lens: sampling transports a particle from noise to data by integrating a learned velocity field, and each sample corresponds to a trajectory with its own dynamical effort. Motivated by classical mechanics, we introduce Kinetic Path Energy (KPE), an action-like, per-sample diagnostic that measures the accumulated kinetic effort along an ordinary differential equation (ODE) trajectory. Empirically, KPE exhibits two robust correspondences: {i} higher KPE predicts stronger semantic fidelity; {ii} high-KPE trajectories land in sparse representation regions. We further provide theoretical guarantees linking trajectory energy to data sparsity. Paradoxically, this correlation is non-monotonic. At sufficiently high energy, generation can degenerate into memorization. Leveraging the closed-form formula of empirical flow matching, we show that extreme energies drive trajectories","title":"A Kinetic Energy Perspective of Flow Matching","url":"https://arxiv.org/abs/2602.07928","vendor":"arxiv_cs_ai"},"summary":"arXiv:2602.07928v2 Announce Type: replace-cross \nAbstract: Flow-based generative models can be viewed through a physics lens: sampling transports a particle from noise to data by integrating a learned velocity field, and each sample corresponds to a trajectory with its own dynamical effort. Motivated by classical mechanics, we introduce Kinetic Path Energy (KPE), an action-like, per-sample diagnostic that measures the accumulated kinetic effort along an ordinary differential equation (ODE) trajectory. Empirically, KPE exhibits two robust correspondences: {i} higher KPE predicts stronger semantic fidelity; {ii} high-KPE trajectories land in sparse representation regions. We further provide theoretical guarantees linking trajectory energy to data sparsity. Paradoxically, this correlation is non-monotonic. At sufficiently high energy, generation can degenerate into memorization. Leveraging the closed-form formula of empirical flow matching, we show that extreme energies drive trajectories","title":"A Kinetic Energy Perspective of Flow Matching","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-01T04:43:13Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2602.07928"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:20379dedbbd5e6870a5890a91a9c19fdc44ea09153afdf2621910c2e68ffd5ed5ffb99a125cc6e635ba52c07dc6a6a9f653ace25987a4509caaf479df7126c07","signer":"crovia.substrate","subject":{"observed_at":"2026-06-01T04:43:13Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2602.07928"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"4ea613c3aa4099343ec297d69ae23b8b8dde18cae460ca3b6dd6dcf25f7ecd1c","leaf_index":164098,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"5837152308150d3f9fff54f23856cbec0f0a7a711324c333be846313819cb137","side":"right"},{"sibling":"5a775eeee3f34a03af4511afec7e02a86be55f580c41b5f934e938a7c22fe3db","side":"left"},{"sibling":"b0d35a864eb419ae8d491155d876ab76999ba4fe52c66c18eada3bc2a4046ee3","side":"right"},{"sibling":"10e2cc519fc1e7bbade808b9cfac05ca775b5a8013a1f164b558bac1ced1677e","side":"right"},{"sibling":"d2ed68514682bda888bd26f500bf818b9f1c0e894fd25ac3c568cf7a35bee4ae","side":"right"},{"sibling":"db716d28ae117a529404e8f1c8ea86faefa948493e597acb82ec3b14ff0636f4","side":"right"},{"sibling":"411a66cd5a7fa8f996afb73d603026ea06f5f72e02002d390e8c35173a12a73e","side":"right"},{"sibling":"fa66353dd6f42c595db53c4b87c558d4cbcc04862c4058c0562cc7d5d9015f15","side":"right"},{"sibling":"7caaac9d7d329e12cd7433a2a627fcb2eaa744feb44b4a8462db35186e31e111","side":"left"},{"sibling":"fc601f0745c37fc5f7c249300e654db05d61bb9059885eeb0b0a5047b5d28408","side":"right"},{"sibling":"6ed9290cdae063f13bfeb71c4c5440595cabb61fd4b39225b9cc913ffb336dd7","side":"right"},{"sibling":"a0446b923d1ce90021e78edff07f6bfc7cc2a1326a565c5f0786b82a24dd0a2a","side":"right"},{"sibling":"e598fd53912c30e58ca8e58d7d8a338fe0f2ecb63fdd99225bc703c499c948ec","side":"right"},{"sibling":"fc4873333221ec8167697f75b6f6a8a08491a8cf18952defb65fb6d4958fa5e7","side":"right"},{"sibling":"05c8a827da2a05549ee3250310777009120c687885816bf6c7c74801bfaa346d","side":"right"},{"sibling":"5ea2f2dc9f046df723b6bd9932d61a9a3d80a76e79ce1b939b3d93ff79b5a91c","side":"left"},{"sibling":"ce41d9b82f34b16efd653dfb3552acc4e2512939e47903e5fc979fbed00c5764","side":"right"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":164217,"merkle_root":"a1098816aea1b60b8fe37b62410469bc5024a2c335bbec4f6ef2add7875dbdf2","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260601T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-01T05:37:41Z","sig_algorithm":"ed25519","signature":"d7f91db1d54b9495c499440c2828f4bd53360555391ce6e25adea5183bc1fa0f697d80708a099d0b0429e6f8cb6c71e7fccf82acb3c84481149974fb26074708","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_9040c4bf787d5cd98613b4311c7aa6dee05ef3d867e9b40cf8090e1d5be0aaeb"}}