{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:MPPW2PBCJ2EKTB3UK526FDEHIK","short_pith_number":"pith:MPPW2PBC","canonical_record":{"source":{"id":"2208.07073","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.GA","submitted_at":"2022-08-15T08:41:56Z","cross_cats_sorted":["gr-qc","hep-ph"],"title_canon_sha256":"db4e3534a82bf49a6279ef53c4503749897334038c28e32291e65fc607726863","abstract_canon_sha256":"a00c807820b03bc2d7759cc537fcf7ea7c09ba0a8efe760806db3e08591e7df3"},"schema_version":"1.0"},"canonical_sha256":"63df6d3c224e88a987745775e28c87428c2b9f7fc237fce410ea2a0319e597df","source":{"kind":"arxiv","id":"2208.07073","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.07073","created_at":"2026-07-05T05:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"2208.07073v3","created_at":"2026-07-05T05:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.07073","created_at":"2026-07-05T05:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"MPPW2PBCJ2EK","created_at":"2026-07-05T05:02:13Z"},{"alias_kind":"pith_short_16","alias_value":"MPPW2PBCJ2EKTB3U","created_at":"2026-07-05T05:02:13Z"},{"alias_kind":"pith_short_8","alias_value":"MPPW2PBC","created_at":"2026-07-05T05:02:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:MPPW2PBCJ2EKTB3UK526FDEHIK","target":"record","payload":{"canonical_record":{"source":{"id":"2208.07073","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.GA","submitted_at":"2022-08-15T08:41:56Z","cross_cats_sorted":["gr-qc","hep-ph"],"title_canon_sha256":"db4e3534a82bf49a6279ef53c4503749897334038c28e32291e65fc607726863","abstract_canon_sha256":"a00c807820b03bc2d7759cc537fcf7ea7c09ba0a8efe760806db3e08591e7df3"},"schema_version":"1.0"},"canonical_sha256":"63df6d3c224e88a987745775e28c87428c2b9f7fc237fce410ea2a0319e597df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:02:13.064016Z","signature_b64":"KpD6AWw9tJxDM/eV8E5/caYClLkVFihc/1Mb4GKECk3XjOkwuCCmVv1TT0gZJ+aOzaNTQa/ChpOCNB50IhKwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63df6d3c224e88a987745775e28c87428c2b9f7fc237fce410ea2a0319e597df","last_reissued_at":"2026-07-05T05:02:13.063576Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:02:13.063576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.07073","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IcjU8NkuepONsKyszRMsVO+OeeV+8P9YJu7Tm7wMFJPhFoKrwPxjlgzEiJRqY5JHtYQXrCru0mpR1ebTg/VtAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T23:04:54.110394Z"},"content_sha256":"126f971508a4fb7f7becb6c73bbca8d6f472488ceff30f915cd344afdb4c4877","schema_version":"1.0","event_id":"sha256:126f971508a4fb7f7becb6c73bbca8d6f472488ceff30f915cd344afdb4c4877"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:MPPW2PBCJ2EKTB3UK526FDEHIK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Models of modified-inertia formulation of MOND","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","hep-ph"],"primary_cat":"astro-ph.GA","authors_text":"Mordehai Milgrom","submitted_at":"2022-08-15T08:41:56Z","abstract_excerpt":"Models of \"modified-inertia\" formulation of MOND are described and applied to nonrelativistic many-body systems. They involve time-nonlocal equations of motion. Momentum, angular momentum, and energy are (nonlocally) defined, whose total values are conserved for isolated systems. The models make all the salient MOND predictions. Yet, they differ from existing \"modified-gravity\" formulations in some second-tier predictions. The models describe correctly the motion of a composite body in a low-acceleration field even when the internal accelerations of its constituents are high. They exhibit a MO"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.07073","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.07073/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iwtOqOogh4Nym4fZg195bjloZ4j6ash0/xl8g0u7Ai/dikyRtn4JYabExWIIBewJeaHcavYl6BPh7oCgsQMSAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T23:04:54.111534Z"},"content_sha256":"715bde0e2d2cb583d09d2650f48adf9c20027bf172a70944585f24a9609e3d6c","schema_version":"1.0","event_id":"sha256:715bde0e2d2cb583d09d2650f48adf9c20027bf172a70944585f24a9609e3d6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MPPW2PBCJ2EKTB3UK526FDEHIK/bundle.json","state_url":"https://pith.science/pith/MPPW2PBCJ2EKTB3UK526FDEHIK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MPPW2PBCJ2EKTB3UK526FDEHIK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T23:04:54Z","links":{"resolver":"https://pith.science/pith/MPPW2PBCJ2EKTB3UK526FDEHIK","bundle":"https://pith.science/pith/MPPW2PBCJ2EKTB3UK526FDEHIK/bundle.json","state":"https://pith.science/pith/MPPW2PBCJ2EKTB3UK526FDEHIK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MPPW2PBCJ2EKTB3UK526FDEHIK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:MPPW2PBCJ2EKTB3UK526FDEHIK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a00c807820b03bc2d7759cc537fcf7ea7c09ba0a8efe760806db3e08591e7df3","cross_cats_sorted":["gr-qc","hep-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.GA","submitted_at":"2022-08-15T08:41:56Z","title_canon_sha256":"db4e3534a82bf49a6279ef53c4503749897334038c28e32291e65fc607726863"},"schema_version":"1.0","source":{"id":"2208.07073","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.07073","created_at":"2026-07-05T05:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"2208.07073v3","created_at":"2026-07-05T05:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.07073","created_at":"2026-07-05T05:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"MPPW2PBCJ2EK","created_at":"2026-07-05T05:02:13Z"},{"alias_kind":"pith_short_16","alias_value":"MPPW2PBCJ2EKTB3U","created_at":"2026-07-05T05:02:13Z"},{"alias_kind":"pith_short_8","alias_value":"MPPW2PBC","created_at":"2026-07-05T05:02:13Z"}],"graph_snapshots":[{"event_id":"sha256:715bde0e2d2cb583d09d2650f48adf9c20027bf172a70944585f24a9609e3d6c","target":"graph","created_at":"2026-07-05T05:02:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2208.07073/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Models of \"modified-inertia\" formulation of MOND are described and applied to nonrelativistic many-body systems. They involve time-nonlocal equations of motion. Momentum, angular momentum, and energy are (nonlocally) defined, whose total values are conserved for isolated systems. The models make all the salient MOND predictions. Yet, they differ from existing \"modified-gravity\" formulations in some second-tier predictions. The models describe correctly the motion of a composite body in a low-acceleration field even when the internal accelerations of its constituents are high. They exhibit a MO","authors_text":"Mordehai Milgrom","cross_cats":["gr-qc","hep-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.GA","submitted_at":"2022-08-15T08:41:56Z","title":"Models of modified-inertia formulation of MOND"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.07073","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:126f971508a4fb7f7becb6c73bbca8d6f472488ceff30f915cd344afdb4c4877","target":"record","created_at":"2026-07-05T05:02:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a00c807820b03bc2d7759cc537fcf7ea7c09ba0a8efe760806db3e08591e7df3","cross_cats_sorted":["gr-qc","hep-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.GA","submitted_at":"2022-08-15T08:41:56Z","title_canon_sha256":"db4e3534a82bf49a6279ef53c4503749897334038c28e32291e65fc607726863"},"schema_version":"1.0","source":{"id":"2208.07073","kind":"arxiv","version":3}},"canonical_sha256":"63df6d3c224e88a987745775e28c87428c2b9f7fc237fce410ea2a0319e597df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63df6d3c224e88a987745775e28c87428c2b9f7fc237fce410ea2a0319e597df","first_computed_at":"2026-07-05T05:02:13.063576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:02:13.063576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KpD6AWw9tJxDM/eV8E5/caYClLkVFihc/1Mb4GKECk3XjOkwuCCmVv1TT0gZJ+aOzaNTQa/ChpOCNB50IhKwDg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:02:13.064016Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.07073","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:126f971508a4fb7f7becb6c73bbca8d6f472488ceff30f915cd344afdb4c4877","sha256:715bde0e2d2cb583d09d2650f48adf9c20027bf172a70944585f24a9609e3d6c"],"state_sha256":"08c977a639d02cdd78f837eca5be4029d5d07473b729c9bb773c0d6d73c51135"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Cin8dIk0b+Puc9pi2YvMd4ultsnouZevk59W44kEloC20PaVBq3OLf8CiiJoYQUUYjNa52wu7IhYn9WWwu2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T23:04:54.119502Z","bundle_sha256":"37380c428f131af1c834b5213b3924d35662397d42ce0dc14d286cde2b4688c6"}}