{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VFS7QA74NOC6A2PFAZP6EDMF2W","short_pith_number":"pith:VFS7QA74","canonical_record":{"source":{"id":"1102.4916","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-24T07:23:58Z","cross_cats_sorted":["math-ph","math.AC","math.DG","math.GR","math.MP"],"title_canon_sha256":"ee8d6e6c897707379b4a3c3da8ad7bb2cc01cf80a13f1b1a2666078aa3a39956","abstract_canon_sha256":"689f5ca143d7c1a4a4710a54f7c48c1af3fef828aaddc6a5c61a4baef7f0f032"},"schema_version":"1.0"},"canonical_sha256":"a965f803fc6b85e069e5065fe20d85d5b0f91c5426efd511f0a518e0b7976172","source":{"kind":"arxiv","id":"1102.4916","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4916","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4916v3","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4916","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"pith_short_12","alias_value":"VFS7QA74NOC6","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VFS7QA74NOC6A2PF","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VFS7QA74","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VFS7QA74NOC6A2PFAZP6EDMF2W","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4916","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-24T07:23:58Z","cross_cats_sorted":["math-ph","math.AC","math.DG","math.GR","math.MP"],"title_canon_sha256":"ee8d6e6c897707379b4a3c3da8ad7bb2cc01cf80a13f1b1a2666078aa3a39956","abstract_canon_sha256":"689f5ca143d7c1a4a4710a54f7c48c1af3fef828aaddc6a5c61a4baef7f0f032"},"schema_version":"1.0"},"canonical_sha256":"a965f803fc6b85e069e5065fe20d85d5b0f91c5426efd511f0a518e0b7976172","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:08.419233Z","signature_b64":"gnAui3uciSFnioXrqo2gsjznXgR4BqQVzvUyz2u8AJZEXp3BY+BTO0lPI1kDRrjis9Gvy2nonDi/tpy9r1WlAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a965f803fc6b85e069e5065fe20d85d5b0f91c5426efd511f0a518e0b7976172","last_reissued_at":"2026-05-18T04:11:08.418505Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:08.418505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4916","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":"2026-05-18T04:11:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"feUxYqkJHB3OlCRQfhowYEwao6ZFt8aQyDT1Oaqfev2l2UfvPP704IMH07mJZJupuICAJb4pr2r++MplhPDIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:38:01.289420Z"},"content_sha256":"6878ecbf7a468724a5b32c4c9067190017cbb002dea1b8a03e7866066898d2a5","schema_version":"1.0","event_id":"sha256:6878ecbf7a468724a5b32c4c9067190017cbb002dea1b8a03e7866066898d2a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VFS7QA74NOC6A2PFAZP6EDMF2W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spencer Operator and Applications: From Continuum Mechanics to Mathematical physics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AC","math.DG","math.GR","math.MP"],"primary_cat":"math.AP","authors_text":"Jean-Fran\\c{c}ois Pommaret (CERMICS)","submitted_at":"2011-02-24T07:23:58Z","abstract_excerpt":"The Spencer operator, introduced by D.C. Spencer fifty years ago, is rarely used in mathematics today and, up to our knowledge, has never been used in engineering applications or mathematical physics. The main purpose of this paper, an extended version of a lecture at the second workshop on Differential Equations by Algebraic Methods (DEAM2, february 9-11, 2011, Linz, Austria) is to prove that the use of the Spencer operator constitutes the common secret of the three following famous books published about at the same time in the beginning of the last century, though they do not seem to have an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4916","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":""},"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":"2026-05-18T04:11:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SENZjVDQwB70S/V3VI6EJ5tcmCXptzBS0zMyozvFTWAD0/Z7evulxXrd3glPCKAR51xa8hwi8URRYdR38XxOBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:38:01.290137Z"},"content_sha256":"4dcf42d58d36455d8f6a6f5d7e6edd84935dfd886e72a2f47fcf5ae2c5b30de3","schema_version":"1.0","event_id":"sha256:4dcf42d58d36455d8f6a6f5d7e6edd84935dfd886e72a2f47fcf5ae2c5b30de3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VFS7QA74NOC6A2PFAZP6EDMF2W/bundle.json","state_url":"https://pith.science/pith/VFS7QA74NOC6A2PFAZP6EDMF2W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VFS7QA74NOC6A2PFAZP6EDMF2W/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":"2026-06-11T22:38:01Z","links":{"resolver":"https://pith.science/pith/VFS7QA74NOC6A2PFAZP6EDMF2W","bundle":"https://pith.science/pith/VFS7QA74NOC6A2PFAZP6EDMF2W/bundle.json","state":"https://pith.science/pith/VFS7QA74NOC6A2PFAZP6EDMF2W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VFS7QA74NOC6A2PFAZP6EDMF2W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VFS7QA74NOC6A2PFAZP6EDMF2W","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":"689f5ca143d7c1a4a4710a54f7c48c1af3fef828aaddc6a5c61a4baef7f0f032","cross_cats_sorted":["math-ph","math.AC","math.DG","math.GR","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-24T07:23:58Z","title_canon_sha256":"ee8d6e6c897707379b4a3c3da8ad7bb2cc01cf80a13f1b1a2666078aa3a39956"},"schema_version":"1.0","source":{"id":"1102.4916","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4916","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4916v3","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4916","created_at":"2026-05-18T04:11:08Z"},{"alias_kind":"pith_short_12","alias_value":"VFS7QA74NOC6","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VFS7QA74NOC6A2PF","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VFS7QA74","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:4dcf42d58d36455d8f6a6f5d7e6edd84935dfd886e72a2f47fcf5ae2c5b30de3","target":"graph","created_at":"2026-05-18T04:11:08Z","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"},"paper":{"abstract_excerpt":"The Spencer operator, introduced by D.C. Spencer fifty years ago, is rarely used in mathematics today and, up to our knowledge, has never been used in engineering applications or mathematical physics. The main purpose of this paper, an extended version of a lecture at the second workshop on Differential Equations by Algebraic Methods (DEAM2, february 9-11, 2011, Linz, Austria) is to prove that the use of the Spencer operator constitutes the common secret of the three following famous books published about at the same time in the beginning of the last century, though they do not seem to have an","authors_text":"Jean-Fran\\c{c}ois Pommaret (CERMICS)","cross_cats":["math-ph","math.AC","math.DG","math.GR","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-24T07:23:58Z","title":"Spencer Operator and Applications: From Continuum Mechanics to Mathematical physics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4916","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":"sha256:6878ecbf7a468724a5b32c4c9067190017cbb002dea1b8a03e7866066898d2a5","target":"record","created_at":"2026-05-18T04:11:08Z","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":"689f5ca143d7c1a4a4710a54f7c48c1af3fef828aaddc6a5c61a4baef7f0f032","cross_cats_sorted":["math-ph","math.AC","math.DG","math.GR","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-24T07:23:58Z","title_canon_sha256":"ee8d6e6c897707379b4a3c3da8ad7bb2cc01cf80a13f1b1a2666078aa3a39956"},"schema_version":"1.0","source":{"id":"1102.4916","kind":"arxiv","version":3}},"canonical_sha256":"a965f803fc6b85e069e5065fe20d85d5b0f91c5426efd511f0a518e0b7976172","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a965f803fc6b85e069e5065fe20d85d5b0f91c5426efd511f0a518e0b7976172","first_computed_at":"2026-05-18T04:11:08.418505Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:08.418505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gnAui3uciSFnioXrqo2gsjznXgR4BqQVzvUyz2u8AJZEXp3BY+BTO0lPI1kDRrjis9Gvy2nonDi/tpy9r1WlAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:08.419233Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4916","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6878ecbf7a468724a5b32c4c9067190017cbb002dea1b8a03e7866066898d2a5","sha256:4dcf42d58d36455d8f6a6f5d7e6edd84935dfd886e72a2f47fcf5ae2c5b30de3"],"state_sha256":"404e5fbf9a6613fe0c7b576db4e2eea75eaea8553ff1a98354d226f38a1e5b62"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"juNYF8U3vrFrrMyHs644UmJCVu6NLCmOwGUfGW5U2KjgmTDqOS8qmEteRQr2FNwQFTiVNkAgyOkWGysb5JxSBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:38:01.294978Z","bundle_sha256":"c2945059aa97de8e22804db406788a6bd6a0fcbf9797249af301ed8b97961bb6"}}