{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VL3Z7PCWFJ4O6TOYW3WBKXOFSH","short_pith_number":"pith:VL3Z7PCW","canonical_record":{"source":{"id":"2504.12199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-16T15:48:34Z","cross_cats_sorted":[],"title_canon_sha256":"3331cf8ea538c273d3479c615fd204226f08d1c21e1e0ee04a1ececc450f2acd","abstract_canon_sha256":"7fb0957edb9976e4c15d0b13d7c71616fb5252713eb73123f6266e84d270055d"},"schema_version":"1.0"},"canonical_sha256":"aaf79fbc562a78ef4dd8b6ec155dc591c9429aff6d06b1baf8abc9c39ad77de8","source":{"kind":"arxiv","id":"2504.12199","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.12199","created_at":"2026-05-25T02:01:03Z"},{"alias_kind":"arxiv_version","alias_value":"2504.12199v2","created_at":"2026-05-25T02:01:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.12199","created_at":"2026-05-25T02:01:03Z"},{"alias_kind":"pith_short_12","alias_value":"VL3Z7PCWFJ4O","created_at":"2026-05-25T02:01:03Z"},{"alias_kind":"pith_short_16","alias_value":"VL3Z7PCWFJ4O6TOY","created_at":"2026-05-25T02:01:03Z"},{"alias_kind":"pith_short_8","alias_value":"VL3Z7PCW","created_at":"2026-05-25T02:01:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VL3Z7PCWFJ4O6TOYW3WBKXOFSH","target":"record","payload":{"canonical_record":{"source":{"id":"2504.12199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-16T15:48:34Z","cross_cats_sorted":[],"title_canon_sha256":"3331cf8ea538c273d3479c615fd204226f08d1c21e1e0ee04a1ececc450f2acd","abstract_canon_sha256":"7fb0957edb9976e4c15d0b13d7c71616fb5252713eb73123f6266e84d270055d"},"schema_version":"1.0"},"canonical_sha256":"aaf79fbc562a78ef4dd8b6ec155dc591c9429aff6d06b1baf8abc9c39ad77de8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:03.549304Z","signature_b64":"N6KWxuKsD8Od3BGTMoNJp0Q4fGyFn9twgLz2SfvJqFSJdKCy18PNzG13FUUJnDz4hfrqLpM+z41n7mdk9e+XAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aaf79fbc562a78ef4dd8b6ec155dc591c9429aff6d06b1baf8abc9c39ad77de8","last_reissued_at":"2026-05-25T02:01:03.548504Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:03.548504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.12199","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-25T02:01:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MzwhHPeSw24L5J6ZRUOgRpemM/TD/L3dnqPKLrJ/zeQm9zaSc0aFEmriWaUJmNN5RRJ6qYhVhGOHz2p5xx6BDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:42:25.714733Z"},"content_sha256":"1fc491e10263dc94bde87c1cbc855a722b9fda7216ee26e72d32c17dd4ea9ef3","schema_version":"1.0","event_id":"sha256:1fc491e10263dc94bde87c1cbc855a722b9fda7216ee26e72d32c17dd4ea9ef3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VL3Z7PCWFJ4O6TOYW3WBKXOFSH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotonicity formulas for minimal submanifolds involving M\\\"obius transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Doanh Pham","submitted_at":"2025-04-16T15:48:34Z","abstract_excerpt":"For a minimal submanifold of the Euclidean space, we prove monotonicity formulas for its (weighted) volume within images of concentric balls under M\\\"obius transformations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.12199","kind":"arxiv","version":2},"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/2504.12199/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":"2026-05-25T02:01:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/i6qUI+cInB3KT9YgvVQMQLhAIA3hskXtmuZ3V3g5sJUsTm2gC2g7rymJcNcdOLUcD3SKUTv5jpjpoHFCfo3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:42:25.715101Z"},"content_sha256":"ca37e5a4cfa86889270613e752c66759522d6ecb0bf4692c01df17f58ae9660d","schema_version":"1.0","event_id":"sha256:ca37e5a4cfa86889270613e752c66759522d6ecb0bf4692c01df17f58ae9660d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VL3Z7PCWFJ4O6TOYW3WBKXOFSH/bundle.json","state_url":"https://pith.science/pith/VL3Z7PCWFJ4O6TOYW3WBKXOFSH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VL3Z7PCWFJ4O6TOYW3WBKXOFSH/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":"2026-07-06T20:42:25Z","links":{"resolver":"https://pith.science/pith/VL3Z7PCWFJ4O6TOYW3WBKXOFSH","bundle":"https://pith.science/pith/VL3Z7PCWFJ4O6TOYW3WBKXOFSH/bundle.json","state":"https://pith.science/pith/VL3Z7PCWFJ4O6TOYW3WBKXOFSH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VL3Z7PCWFJ4O6TOYW3WBKXOFSH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VL3Z7PCWFJ4O6TOYW3WBKXOFSH","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":"7fb0957edb9976e4c15d0b13d7c71616fb5252713eb73123f6266e84d270055d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-16T15:48:34Z","title_canon_sha256":"3331cf8ea538c273d3479c615fd204226f08d1c21e1e0ee04a1ececc450f2acd"},"schema_version":"1.0","source":{"id":"2504.12199","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.12199","created_at":"2026-05-25T02:01:03Z"},{"alias_kind":"arxiv_version","alias_value":"2504.12199v2","created_at":"2026-05-25T02:01:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.12199","created_at":"2026-05-25T02:01:03Z"},{"alias_kind":"pith_short_12","alias_value":"VL3Z7PCWFJ4O","created_at":"2026-05-25T02:01:03Z"},{"alias_kind":"pith_short_16","alias_value":"VL3Z7PCWFJ4O6TOY","created_at":"2026-05-25T02:01:03Z"},{"alias_kind":"pith_short_8","alias_value":"VL3Z7PCW","created_at":"2026-05-25T02:01:03Z"}],"graph_snapshots":[{"event_id":"sha256:ca37e5a4cfa86889270613e752c66759522d6ecb0bf4692c01df17f58ae9660d","target":"graph","created_at":"2026-05-25T02:01:03Z","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/2504.12199/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a minimal submanifold of the Euclidean space, we prove monotonicity formulas for its (weighted) volume within images of concentric balls under M\\\"obius transformations.","authors_text":"Doanh Pham","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-16T15:48:34Z","title":"Monotonicity formulas for minimal submanifolds involving M\\\"obius transformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.12199","kind":"arxiv","version":2},"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":"sha256:1fc491e10263dc94bde87c1cbc855a722b9fda7216ee26e72d32c17dd4ea9ef3","target":"record","created_at":"2026-05-25T02:01:03Z","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":"7fb0957edb9976e4c15d0b13d7c71616fb5252713eb73123f6266e84d270055d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-04-16T15:48:34Z","title_canon_sha256":"3331cf8ea538c273d3479c615fd204226f08d1c21e1e0ee04a1ececc450f2acd"},"schema_version":"1.0","source":{"id":"2504.12199","kind":"arxiv","version":2}},"canonical_sha256":"aaf79fbc562a78ef4dd8b6ec155dc591c9429aff6d06b1baf8abc9c39ad77de8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aaf79fbc562a78ef4dd8b6ec155dc591c9429aff6d06b1baf8abc9c39ad77de8","first_computed_at":"2026-05-25T02:01:03.548504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:01:03.548504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N6KWxuKsD8Od3BGTMoNJp0Q4fGyFn9twgLz2SfvJqFSJdKCy18PNzG13FUUJnDz4hfrqLpM+z41n7mdk9e+XAQ==","signature_status":"signed_v1","signed_at":"2026-05-25T02:01:03.549304Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.12199","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fc491e10263dc94bde87c1cbc855a722b9fda7216ee26e72d32c17dd4ea9ef3","sha256:ca37e5a4cfa86889270613e752c66759522d6ecb0bf4692c01df17f58ae9660d"],"state_sha256":"15e7ca0ff81125a5fafccc14f6afc0800c816fe578798af97e2033f452954ac2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p0CfCzfRF2o3ghZmaoi5h+nZdBrxWE5gZWWloUEK/Jbj/MkMCpok39ITRPH591DoXvNF92qlJ+QgsYycG6A+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T20:42:25.717138Z","bundle_sha256":"ec05bf56b4e0c044060daad904c8ebd1b6cca41e734cd6c2fd9b4ea764472e71"}}