{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:DHMQLO6FTNG4PNV4E6U7KIRATT","short_pith_number":"pith:DHMQLO6F","canonical_record":{"source":{"id":"2506.16549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-19T19:09:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d81ea435d7bcb80f4ba3a0040111083075664b341a1251c47e03501c98b59f15","abstract_canon_sha256":"5be1cb8f79c4228c324d5b30499aadfee0d092a6877c2d87e070349cd8d1e61d"},"schema_version":"1.0"},"canonical_sha256":"19d905bbc59b4dc7b6bc27a9f522209cf4b9a4f475022cae4b7028d1cd079008","source":{"kind":"arxiv","id":"2506.16549","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.16549","created_at":"2026-07-05T11:24:38Z"},{"alias_kind":"arxiv_version","alias_value":"2506.16549v1","created_at":"2026-07-05T11:24:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.16549","created_at":"2026-07-05T11:24:38Z"},{"alias_kind":"pith_short_12","alias_value":"DHMQLO6FTNG4","created_at":"2026-07-05T11:24:38Z"},{"alias_kind":"pith_short_16","alias_value":"DHMQLO6FTNG4PNV4","created_at":"2026-07-05T11:24:38Z"},{"alias_kind":"pith_short_8","alias_value":"DHMQLO6F","created_at":"2026-07-05T11:24:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:DHMQLO6FTNG4PNV4E6U7KIRATT","target":"record","payload":{"canonical_record":{"source":{"id":"2506.16549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-19T19:09:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d81ea435d7bcb80f4ba3a0040111083075664b341a1251c47e03501c98b59f15","abstract_canon_sha256":"5be1cb8f79c4228c324d5b30499aadfee0d092a6877c2d87e070349cd8d1e61d"},"schema_version":"1.0"},"canonical_sha256":"19d905bbc59b4dc7b6bc27a9f522209cf4b9a4f475022cae4b7028d1cd079008","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:24:38.077226Z","signature_b64":"leavNUvCLHwNrK5qSUh16iqkuSv2aIvtWlnRQV/NeVinp57gmdzt8B3Y2hbDtqG0CMdTnTiERpHr3KftMb3GCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19d905bbc59b4dc7b6bc27a9f522209cf4b9a4f475022cae4b7028d1cd079008","last_reissued_at":"2026-07-05T11:24:38.076620Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:24:38.076620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.16549","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:24:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WVr2LeiAvY8lXwR/1h/njaRyM+zs4iZmYHYphrSe3ZYwRnJHPDTc6O6AEM+DGoGA0F43OrPtA4tc6dF7YY1LBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T14:13:12.823078Z"},"content_sha256":"83d1beddd3ed4445ecc5d2a2ff65fb19a11d7ca121a7d5dcd959d265fb528304","schema_version":"1.0","event_id":"sha256:83d1beddd3ed4445ecc5d2a2ff65fb19a11d7ca121a7d5dcd959d265fb528304"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:DHMQLO6FTNG4PNV4E6U7KIRATT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Berezinian expansion and super exterior powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Ekaterina Shemyakova, Maheshan Ekanayaka","submitted_at":"2025-06-19T19:09:15Z","abstract_excerpt":"In the supergeometric setting, the classical identification between differential forms of top degree and volume elements for integration breaks down. To address this, generalized notions of differential forms were introduced: pseudo-differential forms and integral forms (Bernstein-Leites), and $r|s$-forms (Voronov-Zorich). The Baranov-Schwarz transformation transforms pseudo-differential forms into $r|s$-forms. Also, integral $r$-forms are isomorphic to $r|m$-forms for a supermanifold of dimension $n|m$, yet the explicit construction of $r|s$-forms for arbitrary $s$ remains elusive.\n  In this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.16549","kind":"arxiv","version":1},"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/2506.16549/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":"2026-07-05T11:24:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u4B1Dzv7OjlVm8O6KbAhEZpwuL5/2P8Nq73UTBUV6bhr/8qzJ6H9Q2aY+n4bEIDcXPmNTCDto8OJzo/SCVnKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T14:13:12.823600Z"},"content_sha256":"be3e20bd18344ab8c280e301bf6cd6c1076c8bdf0f98b601b6c91fb8510c0f4d","schema_version":"1.0","event_id":"sha256:be3e20bd18344ab8c280e301bf6cd6c1076c8bdf0f98b601b6c91fb8510c0f4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DHMQLO6FTNG4PNV4E6U7KIRATT/bundle.json","state_url":"https://pith.science/pith/DHMQLO6FTNG4PNV4E6U7KIRATT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DHMQLO6FTNG4PNV4E6U7KIRATT/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":"2026-08-23T14:13:12Z","links":{"resolver":"https://pith.science/pith/DHMQLO6FTNG4PNV4E6U7KIRATT","bundle":"https://pith.science/pith/DHMQLO6FTNG4PNV4E6U7KIRATT/bundle.json","state":"https://pith.science/pith/DHMQLO6FTNG4PNV4E6U7KIRATT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DHMQLO6FTNG4PNV4E6U7KIRATT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DHMQLO6FTNG4PNV4E6U7KIRATT","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":"5be1cb8f79c4228c324d5b30499aadfee0d092a6877c2d87e070349cd8d1e61d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-19T19:09:15Z","title_canon_sha256":"d81ea435d7bcb80f4ba3a0040111083075664b341a1251c47e03501c98b59f15"},"schema_version":"1.0","source":{"id":"2506.16549","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.16549","created_at":"2026-07-05T11:24:38Z"},{"alias_kind":"arxiv_version","alias_value":"2506.16549v1","created_at":"2026-07-05T11:24:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.16549","created_at":"2026-07-05T11:24:38Z"},{"alias_kind":"pith_short_12","alias_value":"DHMQLO6FTNG4","created_at":"2026-07-05T11:24:38Z"},{"alias_kind":"pith_short_16","alias_value":"DHMQLO6FTNG4PNV4","created_at":"2026-07-05T11:24:38Z"},{"alias_kind":"pith_short_8","alias_value":"DHMQLO6F","created_at":"2026-07-05T11:24:38Z"}],"graph_snapshots":[{"event_id":"sha256:be3e20bd18344ab8c280e301bf6cd6c1076c8bdf0f98b601b6c91fb8510c0f4d","target":"graph","created_at":"2026-07-05T11:24:38Z","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/2506.16549/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the supergeometric setting, the classical identification between differential forms of top degree and volume elements for integration breaks down. To address this, generalized notions of differential forms were introduced: pseudo-differential forms and integral forms (Bernstein-Leites), and $r|s$-forms (Voronov-Zorich). The Baranov-Schwarz transformation transforms pseudo-differential forms into $r|s$-forms. Also, integral $r$-forms are isomorphic to $r|m$-forms for a supermanifold of dimension $n|m$, yet the explicit construction of $r|s$-forms for arbitrary $s$ remains elusive.\n  In this ","authors_text":"Ekaterina Shemyakova, Maheshan Ekanayaka","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-19T19:09:15Z","title":"Berezinian expansion and super exterior powers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.16549","kind":"arxiv","version":1},"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":"sha256:83d1beddd3ed4445ecc5d2a2ff65fb19a11d7ca121a7d5dcd959d265fb528304","target":"record","created_at":"2026-07-05T11:24:38Z","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":"5be1cb8f79c4228c324d5b30499aadfee0d092a6877c2d87e070349cd8d1e61d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-06-19T19:09:15Z","title_canon_sha256":"d81ea435d7bcb80f4ba3a0040111083075664b341a1251c47e03501c98b59f15"},"schema_version":"1.0","source":{"id":"2506.16549","kind":"arxiv","version":1}},"canonical_sha256":"19d905bbc59b4dc7b6bc27a9f522209cf4b9a4f475022cae4b7028d1cd079008","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19d905bbc59b4dc7b6bc27a9f522209cf4b9a4f475022cae4b7028d1cd079008","first_computed_at":"2026-07-05T11:24:38.076620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:24:38.076620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"leavNUvCLHwNrK5qSUh16iqkuSv2aIvtWlnRQV/NeVinp57gmdzt8B3Y2hbDtqG0CMdTnTiERpHr3KftMb3GCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:24:38.077226Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.16549","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83d1beddd3ed4445ecc5d2a2ff65fb19a11d7ca121a7d5dcd959d265fb528304","sha256:be3e20bd18344ab8c280e301bf6cd6c1076c8bdf0f98b601b6c91fb8510c0f4d"],"state_sha256":"46604d873d0d5b6b0b2a1053b857941bc261f13ee63d6624e42d597cd1aaba61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"feSlaX4c+28zX2XzPYq6Ykvvi7y4YWr3taXR2etgBMAZ30AFUqLO36T6PmLzufwLm0781qt42SEEy/Cfyze7Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T14:13:12.827371Z","bundle_sha256":"5a940da73ce4db5945356ceaad5962850edd2d83af5ee081bfdafa3315cbefbe"}}